Question

Question #1b237

Answer 1

Use `cos(2x) = 1-2sin^2x` to rewrite.

Explanation:

`sin^2x = 1/2(1-cos(2x))`
(this is called a Power Reduction Formula)

So,

`int sin^2x dx = 1/2int (1-cos(2x)) dx`

We can integrate `intcos(2x) dx` by substitution `u = 2x`

so `intcos(2x) dx = 1/2sin(2x) +C` (check this answer by differentiation)

`int sin^2x dx = 1/2int (1-cos(2x)) dx`

`= 1/2(x-1/2sin(2x))+C`

Rewrite to taste.

You may like

`= 1/2x-1/4sin(2x)+C`

or

`= 1/4(2x-sin(2x))+C`