What is the integral from 0 to 2 of xsqrt(2x) ?

The integral from 0 to 2 of xsqrt(2x) is 16/5

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integral from 0 to 2 of xsqrt(2x)

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

\frac{16}{5}

Decimal

3.2

Solution steps

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

Apply Integration By Parts

: [\frac{1}{2} x^{2} x - \int \frac{1}{2 2} x^{\frac{3}{2}} d x]_{0}^{2}

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

\int \frac{1}{2 2} x^{\frac{3}{2}} d x = \frac{1}{5 2} x^{\frac{5}{2}}

= [\frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}]_{0}^{2}

Simplify

[\frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}]_{0}^{2} : [\frac{2 2}{5} x^{2} x]_{0}^{2}

= [\frac{2 2}{5} x^{2} x]_{0}^{2}

Compute the boundaries:

\frac{16}{5}

= \frac{16}{5}

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What is the integral from 0 to 2 of xsqrt(2x) ?
The integral from 0 to 2 of xsqrt(2x) is 16/5