What is the integral from 0 to 2 of (xsqrt(9-x^2)) ?

The integral from 0 to 2 of (xsqrt(9-x^2)) is (27-5sqrt(5))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of (xsqrt(9-x^2))

\int_{0}^{2} (x 9 - x^{2}) d x

\frac{27 - 5 5}{3}

Decimal

5.27322 \dots

Solution steps

\int_{0}^{2} x 9 - x^{2} d x

Apply u-substitution

: \int_{9}^{5} - \frac{u}{2} d u

= \int_{9}^{5} - \frac{u}{2} d u

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

= - \int_{5}^{9} - \frac{u}{2} d u

Take the constant out:

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

= - (- \frac{1}{2} \cdot \int_{5}^{9} u d u)

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9}

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9})

Simplify

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9}

Compute the boundaries:

18 - \frac{10 5}{3}

= \frac{1}{2} (18 - \frac{10 5}{3})

Simplify

= \frac{27 - 5 5}{3}

\int (3 x - 5)^{2} d x

n = 1 \sum \infty \frac{1}{n ^{1.1}}

\int \frac{7}{6 + 7 x} d x

x \to 9 lim (\frac{x + 9}{x - 9})

\frac{d}{d x} (sin (ln (1 - 3 x)))

What is the integral from 0 to 2 of (xsqrt(9-x^2)) ?
The integral from 0 to 2 of (xsqrt(9-x^2)) is (27-5sqrt(5))/3