What is the integral from-3 to 0 of xsqrt(1-x) ?

The integral from-3 to 0 of xsqrt(1-x) is -116/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-3 to 0 of xsqrt(1-x)

\int_{- 3}^{0} x 1 - x d x

- \frac{116}{15}

Decimal Notation

- 7.73333 \dots

Solution steps

\int_{- 3}^{0} x 1 - x d x

Apply u-substitution

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

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

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

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

Take the constant out:

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

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

Expand

(- u + 1) u : - u^{\frac{3}{2}} + u

= - (- \int_{1}^{4} - u^{\frac{3}{2}} + 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_{1}^{4} u^{\frac{3}{2}} d u + \int_{1}^{4} u d u))

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

\int_{1}^{4} u d u = \frac{14}{3}

= - (- (- \frac{62}{5} + \frac{14}{3}))

Simplify

- (- (- \frac{62}{5} + \frac{14}{3})) : - \frac{116}{15}

= - \frac{116}{15}

\int 6 x e^{x} d x

\frac{d}{d x} (8^{x} ln (x))

\frac{\partial}{\partial x} (e^{6 x + 7 y})

\frac{d}{d x} (\frac{2}{1 - 6 x})

\int \frac{1}{9}

What is the integral from-3 to 0 of xsqrt(1-x) ?
The integral from-3 to 0 of xsqrt(1-x) is -116/15