What is the integral from 0 to 1 of x^2*2x ?

The integral from 0 to 1 of x^2*2x is 1/2

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integral from 0 to 1 of x^2*2x

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

= 2 [\frac{x ^{4}}{4}]_{0}^{1}

Compute the boundaries:

\frac{1}{4}

= 2 \cdot \frac{1}{4}

Simplify

= \frac{1}{2}

What is the integral from 0 to 1 of x^2*2x ?
The integral from 0 to 1 of x^2*2x is 1/2