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

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

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

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

f sin (\frac{x}{2})

Solution steps

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

Use the common integral:

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

= f [sin (x)]_{0}^{\frac{x}{2}}

Compute the boundaries:

sin (\frac{x}{2})

= f sin (\frac{x}{2})

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\int_{1}^{3} (\frac{5}{x} - e^{- x}) d x

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\int_{0}^{8} - 6 x^{2} - 6 x + 432 d x

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