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Unit: Integration for physics (Prerequisite)

If f' is the derivative of f, then f is the antiderivative of f'. To find the antiderivative of a function we need to perform some kind of reverse differentiation. Learn about it here.
Indefinite integrals (or antiderivatives) are really just backward differentiation. Therefore, the indefinite integral of eˣ is eˣ+c, the indefinite integral of 1/x is ln(x)+c, the indefinite integral of sin(x) is -cos(x)+c, and the indefinite integral of cos(x) is sin(x)+c.
The fundamental theorem tells us how we can evaluate definite integrals. Now let us put this to use and evaluate some!
u-substitution is an extremely useful technique. Harnessing the power of the chain rule, it allows us to define a new variable (common denoted by the letter u) as a function of x, and obtain a new expression which is (hopefully) easier to integrate.
The area under a rate function gives the net change. This result of the fundamental theorem of calculus is being put here to use with some real-world problems.

About this unit

Certain ideas in physics require the prior knowledge of integration. The big idea of integral calculus is the calculation of the area under a curve using integrals. Let's do a fundamental course of integration.