reduction method to solve the integral sin^2(17x)dx

[xomandi]

Use the reduction formula to solve the integral sin^2(17x)dx

so would it be then... -1/2 cos (17x) sin(17x) + 1/2 int xdx???

 

[soroban]

Hello, xomandi!

Use the reduction formula to solve: .\(\displaystyle \L\int\)\(\displaystyle \sin^2(17x)\,dx\)

What "reduction formula" are they referring to?

This Double-Angle Identity is appropriate: \(\displaystyle \:\sin^2\theta \:=\:\frac{1\,-\,\cos2\theta}{2}\)


Then we have: \(\displaystyle \L\:\frac{1}{2}\int \left[1\,-\,\cos(34x)\right]\,dx\)