0102 ,5 rebmeced ,0102/5/21 no topsgolbredrum

This week went by pretty quickly, and I'm glad there's only one week left of school until Christmas holidays, for me at least :P. So this week, we learned the joys of antiderivatives and integrals. And I'm not being sarcastic this time. So anyway, I'll discuss how to do some antiderivatives and give plenty of examples of how to do their funcztions.

An antiderivative is a general solution.

f ' (x) = f(x) where the antiderivative is f(x)

You always put "plus c" at the end of a solution

The shortcut to the antiderivative is as follows:

If f '(x) =

a x^#

then the antiderivative or f (x) =

((a)/(#+1)) (x^(#+1))

Examples

Find the antiderivative of 3x.

3/2 x^2 + c

the integral of 1/x^3 dx =

x^-3 dx

1/-2 x^-2

-1/2x^2 + c

the integral of x^1/2 dx =

x^1/2 dx

1/1/3/2 x^3/2 = 2/3 x^3/2 + c

If you have a fractional exponent, multiply by the reciprocal to get your coefficient.