Integrals
The definite integral of a function gives us the area under the curve of that function. Another common interpretation is that the integral of a rate function describes the accumulation of the quantity whose rate is given. We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals.
This course contains 20 segments:
Accumulations of change introduction
Approximation with Riemann sums
Summation notation review
Riemann sums in summation notation
Defining integrals with Riemann sums
Fundamental theorem of calculus and accumulation functions
Interpreting the behavior of accumulation functions
Properties of definite integrals
Fundamental theorem of calculus and definite integrals
Reverse power rule
Indefinite integrals of common functions
Definite integrals of common functions
Integrating with u-substitution
Integrating using long division and completing the square
Integrating using trigonometric identities
Some integrals that contain trig functions demand that we manipulate those functions using trig identities in order to find the integral.
Trigonometric substitution
Another super useful technique for computing integrals involves replacing variables with trigonometric functions. This can make things seem a little more complicated at first, but with the help of trigonometric identities, this technique makes certain integrals solvable.
Integration by parts
Integrating using linear partial fractions
Improper integrals
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Length | 20 segments |
Starts | On Demand (Start anytime) |
Cost | Free |
From | Khan Academy |
Download Videos | On all desktop and mobile devices |
Language | English |
Subjects | Mathematics |
Tags | Math |
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Rating | Not enough ratings |
---|---|
Length | 20 segments |
Starts | On Demand (Start anytime) |
Cost | Free |
From | Khan Academy |
Download Videos | On all desktop and mobile devices |
Language | English |
Subjects | Mathematics |
Tags | Math |
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