What is the integral from 0 to 1 of x^2(3x^2) ?

The integral from 0 to 1 of x^2(3x^2) is 3/5

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integral from 0 to 1 of x^2(3x^2)

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

\frac{3}{5}

Solution steps

\int_{0}^{1} x^{2} \cdot 3 x^{2} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{1} x^{2} x^{2} d x

Simplify

x^{2} x^{2} : x^{4}

= 3 \cdot \int_{0}^{1} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{1}

= 3 [\frac{x ^{5}}{5}]_{0}^{1}

Compute the boundaries:

\frac{1}{5}

= 3 \cdot \frac{1}{5}

Simplify

= \frac{3}{5}

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What is the integral from 0 to 1 of x^2(3x^2) ?
The integral from 0 to 1 of x^2(3x^2) is 3/5