What is the integral from-1 to 2 of xsqrt(2+x) ?

The integral from-1 to 2 of xsqrt(2+x) is 46/15

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integral from-1 to 2 of xsqrt(2+x)

\int_{- 1}^{2} x 2 + x d x

\frac{46}{15}

Solution steps

\int_{- 1}^{2} x 2 + x d x

Apply u-substitution

: \int_{1}^{4} (u - 2) u d u

= \int_{1}^{4} (u - 2) u d u

Expand

(u - 2) u : u^{\frac{3}{2}} - 2 u

= \int_{1}^{4} u^{\frac{3}{2}} - 2 u d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{4} u^{\frac{3}{2}} d u - \int_{1}^{4} 2 u d u

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

\int_{1}^{4} 2 u d u = \frac{28}{3}

= \frac{62}{5} - \frac{28}{3}

Simplify

\frac{62}{5} - \frac{28}{3} : \frac{46}{15}

= \frac{46}{15}

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What is the integral from-1 to 2 of xsqrt(2+x) ?
The integral from-1 to 2 of xsqrt(2+x) is 46/15