WEBVTT

1
00:00:00.000 --> 00:00:04.435
Here is the problem: integral of sqrt(x) from 0 to 4.

2
00:00:04.885 --> 00:00:11.259
Evaluate the definite integral of sqrt(x) from x equals 0 to x equals 4.

3
00:00:12.059 --> 00:00:13.986
Start with the definite integral.

4
00:00:14.436 --> 00:00:20.485
the integral of the square root of x dx equals (2 over 3)x to the power 3 over 2).

5
00:00:20.935 --> 00:00:21.922
Antiderivative.

6
00:00:22.372 --> 00:00:24.984
Apply the fundamental theorem of calculus.

7
00:00:25.784 --> 00:00:32.100
So the answer is 16 over 3 approximately 5.3333333.

8
00:00:32.550 --> 00:00:41.420
A definite integral gives the signed area between the curve and the x-axis: area above the axis counts as positive and area below counts as negative.

9
00:00:42.220 --> 00:00:47.143
Differentiated the antiderivative and compared it with the integrand, which checks out.

10
00:00:47.593 --> 00:00:55.105
Adaptive Simpson prime s rule gives 5.333333333, which checks out.