What is the integral from-3 to 3 of (xy^2)/(x^2+1) ?

The integral from-3 to 3 of (xy^2)/(x^2+1) is (18x)/(1+x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-3 to 3 of (xy^2)/(x^2+1)

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

\frac{18 x}{1 + x ^{2}}

Solution steps

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

Take the constant out:

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

= \frac{x}{1 + x ^{2}} \cdot \int_{- 3}^{3} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{- 3}^{3}

= \frac{x}{1 + x ^{2}} [\frac{y ^{3}}{3}]_{- 3}^{3}

Compute the boundaries:

18

= \frac{x}{1 + x ^{2}} \cdot 18

Simplify

= \frac{18 x}{1 + x ^{2}}

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

\int_{0}^{9} x^{\frac{1}{2}} d x

\int_{- 2}^{2} 2 x^{2} - 8 d x

\int_{2}^{3} x d x

\int_{0}^{1} \frac{x ( - x ^{2} + 1 ) ^{\frac{3}{2}}}{3} d x

What is the integral from-3 to 3 of (xy^2)/(x^2+1) ?
The integral from-3 to 3 of (xy^2)/(x^2+1) is (18x)/(1+x^2)