en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (xy)/2

Solution

\int \frac{x y}{2} d x

Solution

\frac{y x ^{2}}{4} + C

Solution steps

\int \frac{x y}{2} d x

Take the constant out:

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

= \frac{y}{2} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Simplify

\frac{y}{2} \cdot \frac{x ^{2}}{2} : \frac{y x ^{2}}{4}

= \frac{y x ^{2}}{4}

Add a constant to the solution

= \frac{y x ^{2}}{4} + C

Popular Examples

integral of 1/(x-2x^2)

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

integral of 2xln^2(x)

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

integral of (2x)/(5+3x^2)

\int \frac{2 x}{5 + 3 x ^{2}} d x

integral of (8+t+6t^2-12t^3)/((3t^2+4)(t^2+7))

\int \frac{8 + t + 6 t ^{2} - 12 t ^{3}}{( 3 t ^{2} + 4 ) ( t ^{2} + 7 )} d t

integral of 5e^{cos(x)}sin(x)

\int 5 e^{c o s (x)} sin (x) d x

Frequently Asked Questions (FAQ)

What is the integral of (xy)/2 ?
The integral of (xy)/2 is (yx^2)/4+C