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

The integral from 0 to 3/2 sqrt(3 of)(x^3)/(sqrt(9-x^2)) is 45/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3/2 sqrt(3 of)(x^3)/(sqrt(9-x^2))

\int_{0}^{\frac{3}{2} 3} \frac{x ^{3}}{9 - x ^{2}} d x

\frac{45}{8}

Decimal Notation

5.625

Solution steps

\int_{0}^{\frac{3}{2} 3} \frac{x ^{3}}{9 - x ^{2}} d x

Apply u-substitution

: \int_{3}^{\frac{3}{2}} u^{2} - 9 d u

= \int_{3}^{\frac{3}{2}} u^{2} - 9 d u

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

= - \int_{\frac{3}{2}}^{3} u^{2} - 9 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_{\frac{3}{2}}^{3} u^{2} d u - \int_{\frac{3}{2}}^{3} 9 d u)

\int_{\frac{3}{2}}^{3} u^{2} d u = \frac{63}{8}

\int_{\frac{3}{2}}^{3} 9 d u = \frac{27}{2}

= - (\frac{63}{8} - \frac{27}{2})

Simplify

- (\frac{63}{8} - \frac{27}{2}) : \frac{45}{8}

= \frac{45}{8}

y = \frac{e ^{x} - e ^{- x}}{2}

\int x^{3} + 3 x - 2 d x

\frac{d}{d t} (\frac{1}{3} t^{3} + \frac{1}{2} t^{2})

\frac{d}{d x} (e^{- 8 x^{2}})

\frac{\partial}{\partial y} (e^{(x + y)} - 1)

What is the integral from 0 to 3/2 sqrt(3 of)(x^3)/(sqrt(9-x^2)) ?
The integral from 0 to 3/2 sqrt(3 of)(x^3)/(sqrt(9-x^2)) is 45/8