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## Homework Statement

Use substitution to show that for any continuous function f,

$$\int_0^{\pi/2} f(\sin x)\,dx = \int_0^{\pi/2} f(\cos x)\,dx.$$

## Homework Equations

$$\cos(\pi/2-x)=\sin x$$

## The Attempt at a Solution

My confusion is that f is inside the integral, and I have no idea if it would change anything.

When I do the substitution normally, I get ##\int_0^{\pi/2} f(\cos u)\,du##, but that doesn't help because it is in terms of u and not x.

Can someone help me understand this?

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