What is the integral from-11 to 0 of xsqrt(25-x) ?

The integral from-11 to 0 of xsqrt(25-x) is -5156/15

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integral from-11 to 0 of xsqrt(25-x)

\int_{- 11}^{0} x 25 - x d x

- \frac{5156}{15}

Decimal Notation

- 343.73333 \dots

Solution steps

\int_{- 11}^{0} x 25 - x d x

Apply u-substitution

: \int_{36}^{25} - (- u + 25) u d u

= \int_{36}^{25} - (- u + 25) u d u

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

= - \int_{25}^{36} - (- u + 25) u d u

Take the constant out:

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

= - (- \int_{25}^{36} (- u + 25) u d u)

Expand

(- u + 25) u : - u^{\frac{3}{2}} + 25 u

= - (- \int_{25}^{36} - u^{\frac{3}{2}} + 25 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_{25}^{36} u^{\frac{3}{2}} d u + \int_{25}^{36} 25 u d u))

\int_{25}^{36} u^{\frac{3}{2}} d u = \frac{9302}{5}

\int_{25}^{36} 25 u d u = \frac{4550}{3}

= - (- (- \frac{9302}{5} + \frac{4550}{3}))

Simplify

- (- (- \frac{9302}{5} + \frac{4550}{3})) : - \frac{5156}{15}

= - \frac{5156}{15}

\frac{d}{d x} (x^{2} + 2 x y + y^{2})

\frac{\partial}{\partial x} (4 sin (x))

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

x^{3} + 2 x - 1

F (x) = 7 x^{6} (x^{4} - 7 x)

What is the integral from-11 to 0 of xsqrt(25-x) ?
The integral from-11 to 0 of xsqrt(25-x) is -5156/15