en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-1/2 y^2

Solution

\int - \frac{1}{2} y^{2} d y

Solution

- \frac{y ^{3}}{6} + C

Solution steps

\int - \frac{1}{2} y^{2} d y

Take the constant out:

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

= - \frac{1}{2} \cdot \int y^{2} d y

Apply the Power Rule

: \frac{y ^{3}}{3}

= - \frac{1}{2} \cdot \frac{y ^{3}}{3}

Simplify

- \frac{1}{2} \cdot \frac{y ^{3}}{3} : - \frac{y ^{3}}{6}

= - \frac{y ^{3}}{6}

Add a constant to the solution

= - \frac{y ^{3}}{6} + C

Graph

Popular Examples

integral of (cos(x))/(2-3sin(x))

\int \frac{cos ( x )}{2 - 3 sin ( x )} d x

integral of (sin^2(x/2)+cot^2(x))

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

integral of 2*(2x+3)^3

\int 2 \cdot (2 x + 3)^{3} d x

integral of (x^2+4x)/(x+2)

\int \frac{x ^{2} + 4 x}{x + 2} d x

integral of (x^3)/(9x^2+1)

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

Frequently Asked Questions (FAQ)

What is the integral of-1/2 y^2 ?
The integral of-1/2 y^2 is -(y^3)/6+C