What is the integral from-11 to 1 of xsqrt(5-x) ?

The integral from-11 to 1 of xsqrt(5-x) is -3152/15

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integral from-11 to 1 of xsqrt(5-x)

\int_{- 11}^{1} x 5 - x d x

- \frac{3152}{15}

Decimal

- 210.13333 \dots

Solution steps

\int_{- 11}^{1} x 5 - x d x

Apply u-substitution

: \int_{16}^{4} - (- u + 5) u d u

= \int_{16}^{4} - (- u + 5) u d u

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

= - \int_{4}^{16} - (- u + 5) u d u

Take the constant out:

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

= - (- \int_{4}^{16} (- u + 5) u d u)

Expand

(- u + 5) u : - u^{\frac{3}{2}} + 5 u

= - (- \int_{4}^{16} - u^{\frac{3}{2}} + 5 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_{4}^{16} u^{\frac{3}{2}} d u + \int_{4}^{16} 5 u d u))

\int_{4}^{16} u^{\frac{3}{2}} d u = \frac{1984}{5}

\int_{4}^{16} 5 u d u = \frac{560}{3}

= - (- (- \frac{1984}{5} + \frac{560}{3}))

Simplify

- (- (- \frac{1984}{5} + \frac{560}{3})) : - \frac{3152}{15}

= - \frac{3152}{15}

\int_{0}^{2} - x^{4} + 2 x^{2} + 8 d x

\int_{5}^{10} \frac{18}{25} x d x

\int_{- 2}^{1} (3 x^{2} + 2) d x

\int_{2}^{4} x x - 2 d x

\int_{0}^{0.8} e^{- x} d x

What is the integral from-11 to 1 of xsqrt(5-x) ?
The integral from-11 to 1 of xsqrt(5-x) is -3152/15