What is the integral from 0 to a of f(a-x) ?

The integral from 0 to a of f(a-x) is f(a^2-(a^2)/2)

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integral from 0 to a of f(a-x)

\int_{0}^{a} f (a - x) d x

f (a^{2} - \frac{a ^{2}}{2})

Solution steps

\int_{0}^{a} f (a - 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}^{a} a - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= f (\int_{0}^{a} a d x - \int_{0}^{a} x d x)

\int_{0}^{a} a d x = a^{2}

\int_{0}^{a} x d x = \frac{a ^{2}}{2}

= f (a^{2} - \frac{a ^{2}}{2})

\int_{2}^{6} (x^{2} + 5) d x

\int_{1}^{2} ln^{2} (x) d x

\int_{1}^{2} (x^{2} - 1) d x

\int_{1}^{x} e^{t^{2}} d t

\int_{0}^{2} x^{2} f (x^{3} + 1) d x

What is the integral from 0 to a of f(a-x) ?
The integral from 0 to a of f(a-x) is f(a^2-(a^2)/2)