Calculus Integration - 'u' Substitution - Definite Integrals - 10 Examples

Walk-through of 10 examples solving for definite integrals using 'u' substitution.

0:00 Example 1: integral of dt/(tln(t) from e to e^2
0:49 Example 2: integral of (cos((x+1)^(1/2))/(x+1)^(1/2))*dx from 0 to 8
1:57 Example 3: Find the area of the region bounded by y=x/(x^2 + 16), y=0, x=0, and x=2.
3:08 Example 4: Find the area of the region bounded by y=x/(x^4 + 16), y=0, x=0, and x=2.
4:21 Example 5: Integral of (sin(πln(x))/x)*dx from 1 to e^(1/2)
5:43 Example 6: Integral of 2^(sin(x^(1/2))*cos(x^(1/2))/x^(1/2)*dx from π^2/16 to π^2/9
7:29 Example 7: Find the area of the region bounded by y=(2+sin(x/2))^2*cos(x/2), the x-axis, and the lines x=0 and x=π.
9:14 Example 8: Integral of x^3(x^2 + 1)^(-1/2)*dx from 0 to 4
11:15 Example 9: Integral of (sin(x))^4*dx from 0 to π/2
13:29 Example 10: Integral of sin(x)^5*dx from π/4 to π

The best way to learn how to solve a Calculus problem is to understand examples. This video has NO AUDIO. Problems should be clear and easy to follow.

There are often multiple ways to get to the same answer, so don’t be concerned if your path is different, as long as the final answer is the same.

#calculus #apcalculus #integration #averagevalue