What is the integral from 0 to sqrt(y of)xy^2 ?

The integral from 0 to sqrt(y of)xy^2 is (y^3)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to sqrt(y of)xy^2

\int_{0}^{y} x y^{2} d x

\frac{y ^{3}}{2}

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{y}{2}

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

Simplify

= \frac{y ^{3}}{2}

\int_{1}^{8} (t^{2} - 4 t - 12) d t

\int_{0}^{1} 1 x + 6 d x

\int_{0}^{t} t sin (t) d t

\int_{0}^{4} x^{2} + 2 d x

\int_{0}^{2} x 1 - x^{2} d x

What is the integral from 0 to sqrt(y of)xy^2 ?
The integral from 0 to sqrt(y of)xy^2 is (y^3)/2