What is the integral from x to 2 of (xy)/2 ?

The integral from x to 2 of (xy)/2 is (x(4-x^2))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from x to 2 of (xy)/2

\int_{x}^{2} \frac{x y}{2} d y

\frac{x ( 4 - x ^{2} )}{4}

Solution steps

\int_{x}^{2} \frac{x y}{2} d y

Take the constant out:

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

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

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{x}^{2}

= \frac{x}{2} [\frac{y ^{2}}{2}]_{x}^{2}

Compute the boundaries:

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

= \frac{x}{2} (2 - \frac{x ^{2}}{2})

Simplify

= \frac{x ( 4 - x ^{2} )}{4}

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

\int_{2}^{3} (\frac{4}{x ^{2}} - 3)^{2} d x

\int_{2}^{4} (25 - x^{2})^{2} d x

\int_{2}^{3} t 1 + 4 t^{2} d t

\int_{0}^{\frac{1}{10}} e^{- x^{2}} d x

What is the integral from x to 2 of (xy)/2 ?
The integral from x to 2 of (xy)/2 is (x(4-x^2))/4