What is the integral from 0 to pi/2 of f(cos(x)) ?

The integral from 0 to pi/2 of f(cos(x)) is f

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integral from 0 to pi/2 of f(cos(x))

\int_{0}^{\frac{π}{2}} f (cos (x)) d x

f

Solution steps

\int_{0}^{\frac{π}{2}} f cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= f \cdot \int_{0}^{\frac{π}{2}} cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= f [sin (x)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= f \cdot 1

Simplify

= f

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What is the integral from 0 to pi/2 of f(cos(x)) ?
The integral from 0 to pi/2 of f(cos(x)) is f