What is the integral from 7 to 8 of xsqrt(x-7) ?

The integral from 7 to 8 of xsqrt(x-7) is 76/15

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integral from 7 to 8 of xsqrt(x-7)

\int_{7}^{8} x x - 7 d x

\frac{76}{15}

Decimal

5.06666 \dots

Solution steps

\int_{7}^{8} x x - 7 d x

Apply u-substitution

: \int_{0}^{1} (u + 7) u d u

= \int_{0}^{1} (u + 7) u d u

Expand

(u + 7) u : u^{\frac{3}{2}} + 7 u

= \int_{0}^{1} u^{\frac{3}{2}} + 7 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_{0}^{1} u^{\frac{3}{2}} d u + \int_{0}^{1} 7 u d u

\int_{0}^{1} u^{\frac{3}{2}} d u = \frac{2}{5}

\int_{0}^{1} 7 u d u = \frac{14}{3}

= \frac{2}{5} + \frac{14}{3}

Simplify

\frac{2}{5} + \frac{14}{3} : \frac{76}{15}

= \frac{76}{15}

\frac{\partial}{\partial x} (y x + y + z)

\int 7 x cos (x) d x

\frac{d}{d t} (t - t^{2})

\frac{4}{( s - 2 ) ^{2}}

\frac{d}{d x} (\frac{e ^{2 x}}{x + 1})

What is the integral from 7 to 8 of xsqrt(x-7) ?
The integral from 7 to 8 of xsqrt(x-7) is 76/15