What is the integral from 4 to 5 of xsqrt(x-4) ?

The integral from 4 to 5 of xsqrt(x-4) is 46/15

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integral from 4 to 5 of xsqrt(x-4)

\int_{4}^{5} x x - 4 d x

\frac{46}{15}

Decimal

3.06666 \dots

Solution steps

\int_{4}^{5} x x - 4 d x

Apply u-substitution

: \int_{0}^{1} (u + 4) u d u

= \int_{0}^{1} (u + 4) u d u

Expand

(u + 4) u : u^{\frac{3}{2}} + 4 u

= \int_{0}^{1} u^{\frac{3}{2}} + 4 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} 4 u d u

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

\int_{0}^{1} 4 u d u = \frac{8}{3}

= \frac{2}{5} + \frac{8}{3}

Simplify

\frac{2}{5} + \frac{8}{3} : \frac{46}{15}

= \frac{46}{15}

\frac{d}{d x} (- 0.5 x^{2} + 56 x + 20)

\frac{( 4 - y )}{( 2 ^{y} + 3 )}

\int (- 3 \cdot x + 2) \cdot e^{- x} d x

\int sin^{3} (3 x) cos^{- 2} (3 x) d x

\frac{d}{d x} ((\frac{x}{7} + \frac{7}{x})^{7})

What is the integral from 4 to 5 of xsqrt(x-4) ?
The integral from 4 to 5 of xsqrt(x-4) is 46/15