What is the integral from 0 to 7 of xsqrt(x+2) ?

The integral from 0 to 7 of xsqrt(x+2) is (16sqrt(2)+1458)/(15)-36

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integral from 0 to 7 of xsqrt(x+2)

\int_{0}^{7} x x + 2 d x

\frac{16 2 + 1458}{15} - 36

Decimal Notation

62.70849 \dots

Solution steps

\int_{0}^{7} x x + 2 d x

Apply u-substitution

: \int_{2}^{9} (u - 2) u d u

= \int_{2}^{9} (u - 2) u d u

Expand

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

= \int_{2}^{9} 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_{2}^{9} u^{\frac{3}{2}} d u - \int_{2}^{9} 2 u d u

\int_{2}^{9} u^{\frac{3}{2}} d u = \frac{486 - 8 2}{5}

\int_{2}^{9} 2 u d u = 2 (18 - \frac{4 2}{3})

= \frac{486 - 8 2}{5} - 2 (18 - \frac{4 2}{3})

Simplify

\frac{486 - 8 2}{5} - 2 (18 - \frac{4 2}{3}) : \frac{16 2 + 1458}{15} - 36

= \frac{16 2 + 1458}{15} - 36

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What is the integral from 0 to 7 of xsqrt(x+2) ?
The integral from 0 to 7 of xsqrt(x+2) is (16sqrt(2)+1458)/(15)-36