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Hi! START HERE: Course overview
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Antiderivatives and indefinite integrals
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Indefinite integrals
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Properties of integrals
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Find f given f''
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Find f given f'''
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Initial value problems
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Find f given f'' and initial conditions
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Definite integrals
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Area under or enclosed by the graph
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Definite integrals of even functions
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Definite integrals of odd functions
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Summation notation, finding the sum
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Summation notation, expanding
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Summation notation, collapsing
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Riemann sums, left endpoints
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Riemann sums, right endpoints
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Riemann sums, midpoints
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Over and underestimation
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Limit process to find area on [a,b]
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Limit process to find area on [-a,a]
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Trapezoidal rule
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Simpson's rule
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Midpoint rule error bound
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Trapezoidal rule error bound
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Simpson's rule error bound
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Part 1
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Part 2
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Net change theorem
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U-substitution
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U-substitution in definite integrals
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Integration by parts
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Integration by parts two times
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Integration by parts three times
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Integration by parts with u-substitution
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Prove the reduction formula
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Tabular integration
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Distinct linear factors
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Distinct linear factors, example 2
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Distinct linear factors, example 3
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Repeated linear factors
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Rationalizing substitutions
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How to factor a difficult denominator
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Two ways to find the constants
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Trigonometric integrals
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Trigonometric integrals, example 2
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sin^m cos^n, odd m
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sin^m cos^n, odd n
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sin^m cos^n, m and n even
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tan^m sec^n, odd m
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tan^m sec^n, even n
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tan^m sec^n, even n, example 2
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sin(mx) cos(nx)
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sin(mx) sin(nx)
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cos(mx) cos(nx)
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Hyperbolic integrals
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Inverse hyperbolic integrals
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Trigonometric substitution setup
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Trigonometric substitution with secant
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Trigonometric substitution with sine
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Trigonometric substitution with sine, example 2
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Trigonometric substitution with tangent
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Trigonometric substitution with tangent, example 2
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What makes an integral improper?
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Case 1 [a,infinity)
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Case 2 (-infinity,b]
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Case 3 (-infinity,infinity)
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Case 4 (discontinuity at b)
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Case 5 (discontinuity at a)
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Case 6 (discontinuity between a and b)
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Comparison theorem
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Integrals using reduction formulas
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Upper and lower curves
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Left and right curves
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Sketching the area between curves
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Dividing the area between curves into equal parts
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Arc length of a curve in the form y=f(x)
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Arc length of a curve in the form x=g(y)
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Arc length using simpson's rule
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Average value
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Mean value theorem for integrals
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Surface area of revolution
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Surface area of revolution using simpson's ule
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Surface of revolution equation
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Volume of revolution, major axes of revolution
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Disks, horizontal axis
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Disks, vertical axis
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Disks, vertical axis, example 2
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Disks, volume of the frustum
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Washers, horizontal axis
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Washers, horizontal axis, example 2
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Washers, vertical axis
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Cylindrical shells, horizontal axis
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Cylindrical shells, vertical axis
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Cylindrical shells, vertical axis, example 2
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Work done to lift a mass or weight
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Work done on elastic springs
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Work done to empty a tank
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Work done by a variable force
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Moments of the system
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Moments of the system, x-axis
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Center of mass of the system
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Center of mass of the system, x-axis
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Hydrostatic pressure
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Hydrostatic force
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Vertical motion
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Rectilinear motion
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Centroids of plane regions
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Centroids of plane regions using simpson's rule
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Area of the triangle with the given vertices
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Single deposit, compounded n times, future value
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Single deposit, compounded n times, present value
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Single deposit, compounded continuously, future value
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Single deposit, compounded continuously, present value
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Income stream, compounded continuously, future value
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Income stream, compounded continuously, present value
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Consumer and producer surplus
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Probability density
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Cardiac output
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Cardiac output using simpson's rule
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Poiseuille's law
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Theorem of pappus
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Eliminating the parameter
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Derivative of a parametric curve
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Second derivative of a parametric curve
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Sketching parametric curves by plotting points
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Tangent line to the parametric curve
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Area under a parametric curve
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Area under one arc or loop of a parametric curve
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Arc length of a parametric curve
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Arc length, particle motion
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Arc length, simpson's rule
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Surface area of revolution of a parametric curve, horizontal axis
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Surface area of revolution of a parametric curve, vertical axis
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Volume of revolution of a parametric curve
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Converting to polar coordinates
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Converting rectangular equations
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Converting polar equations
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Distance between polar points
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Sketching polar curves
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Sketching polar curves from cartesian curves
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Tangent line to the polar curve
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Vertical and horizontal tangent lines to the polar curve
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Intersection of polar curves
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Area inside a polar curve
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Area bounded by one loop of a polar curve
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Area between polar curves
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Area inside both polar curves
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Arc length of a polar curve
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Arc length of a polar curve, example 2
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Surface area of revolution of a polar curve
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Listing the first terms
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Calculating the first terms
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Formula for the general term
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Convergence of a sequence
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Limit of a convergent sequence
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Increasing, decreasing, and not monotonic
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Bounded sequences
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Calculating the first terms of a sequence of partial sums
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Sum of the sequence of partial sums
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Geometric series test
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Sum of the geometric series
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Values for which the series converges
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Geometric series for repeating decimals
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Convergence of a telescoping series
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Sum of a telescoping series
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Limit vs. sum of the series
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Integral test
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p-series test
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nth term test
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Comparison test
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Limit comparison test
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Error or remainder of a series
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Ratio test
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Ratio test with factorials
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Root test
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Absolute and conditional convergence
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Alternating series test
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Alternating series estimation theorem
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Power series representation
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Power series multiplication
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Power series division
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Power series differentiation
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Interval of convergence
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Estimating definite integrals
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Estimating indefinite integrals
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Binomial series
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Taylor series
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Radius and interval of convergence of a Taylor series
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Taylor's inequality
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Maclaurin series
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Sum of the Maclaurin series
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Radius and interval of convergence of a Maclaurin series
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Indefinite integral as an infinite series
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Maclaurin series to estimate an indefinite integral
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Maclaurin series to estimate a definite integral
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Maclaurin series to evaluate a limit
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Wrap-up