Suppose that f is a continuous function and that S1−1f (x)dx = π. What is the valueofSπ0f (cos(x)) sin(x)dx?A. 0B. -πC. πD. 2πE. The integral is undefined

The integral ∫ from -1 to 1 f(x) dx is given to be π.

We want to find the value of ∫ from 0 to π f(cos(x)) sin(x) dx.

We can use the substitution method to solve this. Let's set u = cos(x). Then, du = -sin(x) dx.

When x = 0, u = cos(0) = 1. When x = π, u = cos(π) = -1.

So, the integral ∫ from 0 to π f(cos(x)) sin(x) dx becomes - ∫ from 1 to -1 f(u) du.

But, we know that the integral of a function from a to b is the negative of the integral from b to a.

So, - ∫ from 1 to -1 f(u) du = ∫ from -1 to 1 f(u) du = π.

Therefore, the value of ∫ from 0 to π f(cos(x)) sin(x) dx is π.

So, the answer is C. π.