What is the integral from 0 to 3 of xf(x^2) ?

The integral from 0 to 3 of xf(x^2) is (81f)/4

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integral from 0 to 3 of xf(x^2)

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

\frac{81 f}{4}

Solution steps

\int_{0}^{3} x f x^{2} d x

Take the constant out:

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

= f \cdot \int_{0}^{3} x x^{2} d x

Simplify

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

= f \cdot \int_{0}^{3} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{0}^{3}

= f [\frac{x ^{4}}{4}]_{0}^{3}

Compute the boundaries:

\frac{81}{4}

= f \frac{81}{4}

Simplify

= \frac{81 f}{4}

\int_{0}^{2} 4 x^{2} - 2 x^{3} d x

\frac{d}{d x} (x (x - 3)^{2})

y = x^{2}, y = - x^{2} + 4 x

\int 12 sin^{6} (x) cos^{3} (x) d x

f (x) = x^{\frac{5}{11}} (x - 5)^{2}

What is the integral from 0 to 3 of xf(x^2) ?
The integral from 0 to 3 of xf(x^2) is (81f)/4