What is the integral from-2 to 1 of x/(sqrt(2-x)) ?

The integral from-2 to 1 of x/(sqrt(2-x)) is -2/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-2 to 1 of x/(sqrt(2-x))

\int_{- 2}^{1} \frac{x}{2 - x} d x

- \frac{2}{3}

Decimal Notation

- 0.66666 \dots

Solution steps

\int_{- 2}^{1} \frac{x}{2 - x} d x

Apply u-substitution

: \int_{2}^{1} - 2 (- u^{2} + 2) d u

= \int_{2}^{1} - 2 (- u^{2} + 2) d u

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

= - \int_{1}^{2} - 2 (- u^{2} + 2) d u

Take the constant out:

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

= - (- 2 \cdot \int_{1}^{2} - u^{2} + 2 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

= - (- 2 (- \int_{1}^{2} u^{2} d u + \int_{1}^{2} 2 d u))

\int_{1}^{2} u^{2} d u = \frac{7}{3}

\int_{1}^{2} 2 d u = 2

= - (- 2 (- \frac{7}{3} + 2))

Simplify

- (- 2 (- \frac{7}{3} + 2)) : - \frac{2}{3}

= - \frac{2}{3}

\int_{0}^{300} 2 x d x

\int_{\frac{1}{e}}^{e} ∣ ln (x) ∣ (x + 1) d x

\int_{2}^{7} (x^{2} - 2 x) d x

\int_{0}^{2} (x^{3} + 3 x^{2}) d x

\int_{- 3}^{3} \frac{1}{9 + x ^{2}} d x

What is the integral from-2 to 1 of x/(sqrt(2-x)) ?
The integral from-2 to 1 of x/(sqrt(2-x)) is -2/3