What is the integral from 4 to 13 of 6xsqrt(x-4) ?

The integral from 4 to 13 of 6xsqrt(x-4) is 5076/5

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integral from 4 to 13 of 6xsqrt(x-4)

\int_{4}^{13} 6 x x - 4 d x

\frac{5076}{5}

Decimal Notation

1015.2

Solution steps

\int_{4}^{13} 6 x x - 4 d x

Take the constant out:

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

= 6 \cdot \int_{4}^{13} x x - 4 d x

Apply u-substitution

: \int_{0}^{9} (u + 4) u d u

= 6 \cdot \int_{0}^{9} (u + 4) u d u

Expand

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

= 6 \cdot \int_{0}^{9} 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

= 6 (\int_{0}^{9} u^{\frac{3}{2}} d u + \int_{0}^{9} 4 u d u)

\int_{0}^{9} u^{\frac{3}{2}} d u = \frac{486}{5}

\int_{0}^{9} 4 u d u = 72

= 6 (\frac{486}{5} + 72)

Simplify

6 (\frac{486}{5} + 72) : \frac{5076}{5}

= \frac{5076}{5}

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What is the integral from 4 to 13 of 6xsqrt(x-4) ?
The integral from 4 to 13 of 6xsqrt(x-4) is 5076/5