What is the integral from 1 to 3 of x^2*f(x^3) ?

The integral from 1 to 3 of x^2*f(x^3) is (364f)/3

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integral from 1 to 3 of x^2*f(x^3)

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

\frac{364 f}{3}

Solution steps

\int_{1}^{3} x^{2} f x^{3} d x

Take the constant out:

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

= f \cdot \int_{1}^{3} x^{2} x^{3} d x

Simplify

x^{2} x^{3} : x^{5}

= f \cdot \int_{1}^{3} x^{5} d x

Apply the Power Rule

: [\frac{x ^{6}}{6}]_{1}^{3}

= f [\frac{x ^{6}}{6}]_{1}^{3}

Compute the boundaries:

\frac{364}{3}

= f \frac{364}{3}

Simplify

= \frac{364 f}{3}

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What is the integral from 1 to 3 of x^2*f(x^3) ?
The integral from 1 to 3 of x^2*f(x^3) is (364f)/3