en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of-xy^2

Solution

\int - x y^{2} d x

Solution

- \frac{y ^{2} x ^{2}}{2} + C

Solution steps

\int - x y^{2} d x

Take the constant out:

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

= - y^{2} \cdot \int x d x

Apply the Power Rule

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

= - \frac{y ^{2} x ^{2}}{2} + C

Graph

Popular Examples

integral of (12)/(x^2+9)

\int \frac{12}{x ^{2} + 9} d x

integral of ((x^3-8))/(x-2)

\int \frac{( x ^{3} - 8 )}{x - 2} d x

integral of (x+ln(x^2))/x

\int \frac{x + ln ( x ^{2} )}{x} d x

integral of 1/((\sqrt[3]{x))}

\int \frac{1}{( 3 x )} d x

integral of (10)/(xln(x))

\int \frac{10}{x ln ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of-xy^2 ?
The integral of-xy^2 is -(y^2x^2)/2+C