# Thread: Show two integrals are equal

1. ## Show two integrals are equal

How do I show that

$\int_{0}^{\pi/2}&space;sin(2x)^{2n-1}&space;dx&space;=&space;\int_{0}^{\pi/2}&space;sin(x)^{2n-1}&space;dx$

I've tried the substitution u = 2theta but this ends up changing the limits. I suspect I have to make an argument from symmetry?

2. Originally Posted by StaryNight
How do I show that

$\int_{0}^{\pi/2}&space;sin(2x)^{2n-1}&space;dx&space;=&space;\int_{0}^{\pi/2}&space;sin(x)^{2n-1}&space;dx$

I've tried the substitution u = 2theta but this ends up changing the limits. I suspect I have to make an argument from symmetry?
Yes, make the substitution and then use a symmetry argument.