What is the integral from 0 to y of 8xy ?

The integral from 0 to y of 8xy is 4y^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to y of 8xy

\int_{0}^{y} 8 x y d x

4 y^{3}

Solution steps

\int_{0}^{y} 8 x y d x

Take the constant out:

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

= 8 y \cdot \int_{0}^{y} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{y}

= 8 y [\frac{x ^{2}}{2}]_{0}^{y}

Compute the boundaries:

\frac{y ^{2}}{2}

= 8 y \frac{y ^{2}}{2}

Simplify

= 4 y^{3}

\int_{0}^{4} (x^{2}) d x

\int_{6}^{11} \frac{1}{x ^{2}} d x

\int_{0}^{13} ∣ 11 - x ∣ d x

\int_{0}^{1} x + y d x

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

What is the integral from 0 to y of 8xy ?
The integral from 0 to y of 8xy is 4y^3