What is the integral from 0 to 18 of xsqrt(18-x) ?

The integral from 0 to 18 of xsqrt(18-x) is -(1944sqrt(2))/5+648sqrt(2)

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integral from 0 to 18 of xsqrt(18-x)

\int_{0}^{18} x 18 - x d x

- \frac{1944 2}{5} + 6482

Decimal Notation

366.56415 \dots

Solution steps

\int_{0}^{18} x 18 - x d x

Apply u-substitution

: \int_{18}^{0} - (- u + 18) u d u

= \int_{18}^{0} - (- u + 18) u d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{18} - (- u + 18) u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \int_{0}^{18} (- u + 18) u d u)

Expand

(- u + 18) u : - u^{\frac{3}{2}} + 18 u

= - (- \int_{0}^{18} - u^{\frac{3}{2}} + 18 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}^{18} u^{\frac{3}{2}} d u + \int_{0}^{18} 18 u d u))

\int_{0}^{18} u^{\frac{3}{2}} d u = \frac{1944 2}{5}

\int_{0}^{18} 18 u d u = 6482

= - (- (- \frac{1944 2}{5} + 6482))

Simplify

= - \frac{1944 2}{5} + 6482

\frac{1}{( s - 2 )}

\frac{d}{d x} (\frac{x}{x + 4})

\int \frac{1 + e ^{2 x}}{e ^{x - 1}} d x

\int 1 - \frac{3}{14 - x} d x

What is the integral from 0 to 18 of xsqrt(18-x) ?
The integral from 0 to 18 of xsqrt(18-x) is -(1944sqrt(2))/5+648sqrt(2)