WEBVTT

1
00:00:00.000 --> 00:00:02.926
Here is the problem: integral of cos(x).

2
00:00:03.376 --> 00:00:08.322
Find the indefinite integral (antiderivative) of cos(x) with respect to x.

3
00:00:09.122 --> 00:00:10.608
Start with the integral.

4
00:00:11.058 --> 00:00:14.286
the integral of cos x dx equals sin x.

5
00:00:14.736 --> 00:00:17.720
Simplify and add the constant of integration.

6
00:00:18.520 --> 00:00:20.645
So the answer is sin(x) plus C.

7
00:00:21.095 --> 00:00:32.322
An antiderivative F satisfies F prime of x equals f(x). Because the derivative of any constant is 0, every antiderivative differs by a constant C.

8
00:00:33.122 --> 00:00:38.985
Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.