find the integral of the following

Question

1. sin^3(x) 2. Cos^3(x)

Answer 1

Question: find the integral of the following. 1. sin^3(x) 2. Cos^3(x)

1) Write sin^3(x) as sin(x)(sin^2) = sin(x)(1 - cos^2(x)) = sin(x) - sin(x).cos^2(x)

int sin^3(x) = int sin(x) - sin(x).cos^2(x)

= -cos(x) + (1/3)cos^3(x)

2) Write cos^3(x) as cos(x).cos^2(x) = cos(x)(1 - sin^2(x)) = cos(x) - cos(x).sin^2(x)

int cos^3(x) = int cos(x) - cos(x).sin^2(x)

= sin(x) - (1/3)sin^3(x)