How do you evaluate the definite integral $int sin(4x)$ from $[0,pi/8]$ ?

Question

3253 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-04T03:04:44

$1/4$

This is a fairly common integral.

$intsin(ax)dx=-1/acos(ax)$ where $a$ is any constant.

So,

$int_0^(pi/8)sin(4x)dx=-1/4cos4x|_0^(pi/8)$

Evaluating, we get

$-1/4cos((4pi)/8)-(-1/4cos(0))=-1/4cos(pi/2)+1/4cos(0)=1/4$

As $cos0=1$

How do you evaluate the definite integral int sin(4x)int sin(4x) from [0,pi/8][0,pi/8]?