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

The integral from 0 to 1 of x*2x is 2/3

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integral from 0 to 1 of x*2x

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

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

\int_{0}^{1} x \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} xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

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

= 2 [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= 2 \cdot \frac{1}{3}

Simplify

= \frac{2}{3}

6^{2^{x^{2}}}

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

\int (\frac{2}{1 + 2 x}) d x

\frac{d}{d y} (\frac{3 x}{2 y})

\int \frac{1}{sin ^{2} ( x ) + tan ^{2} ( x )} d x

What is the integral from 0 to 1 of x*2x ?
The integral from 0 to 1 of x*2x is 2/3