WEBVTT

1
00:00:00.000 --> 00:00:04.005
Here is the problem: integral of e to the power negative x.

2
00:00:04.455 --> 00:00:10.968
Find the indefinite integral (antiderivative) of e to the power negative x with respect to x.

3
00:00:11.768 --> 00:00:13.196
Start with the integral.

4
00:00:13.646 --> 00:00:21.843
Exponential rule: the integral of eᵘ du equals eᵘ (divide by the inner slope).

5
00:00:22.293 --> 00:00:25.335
Simplify and add the constant of integration.

6
00:00:26.135 --> 00:00:29.978
So the answer is -(1 / e to the power x plus C.

7
00:00:30.428 --> 00:00:41.457
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
00:00:42.257 --> 00:00:48.062
Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.