WEBVTT

1
00:00:00.000 --> 00:00:03.599
Here is the problem: the integral of sin(x) dx.

2
00:00:04.049 --> 00:00:09.018
Find the indefinite integral (antiderivative) of sin(x) with respect to x.

3
00:00:09.818 --> 00:00:11.246
Start with the integral.

4
00:00:11.696 --> 00:00:15.202
the integral of sin x dx equals negative cos x.

5
00:00:15.652 --> 00:00:18.682
Simplify and add the constant of integration.

6
00:00:19.482 --> 00:00:22.164
So the answer is negative cos(x) plus C.

7
00:00:22.614 --> 00:00:33.458
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
00:00:34.258 --> 00:00:40.272
Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.