What is the integral from 0 to y of x*(2x)/(y^2) ?

The integral from 0 to y of x*(2x)/(y^2) is (2y)/3

Popular >

integral from 0 to y of x*(2x)/(y^2)

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

\frac{2 y}{3}

Solution steps

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

Take the constant out:

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

= \frac{2}{y ^{2}} \cdot \int_{0}^{y} xx d x

Simplify

xx : x^{2}

= \frac{2}{y ^{2}} \cdot \int_{0}^{y} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{y}

= \frac{2}{y ^{2}} [\frac{x ^{3}}{3}]_{0}^{y}

Compute the boundaries:

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

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

Simplify

= \frac{2 y}{3}

\int_{- 1}^{0} - sin (nπ x) d x

\int_{0}^{a} x sin^{2} (\frac{2 π x}{a}) d x

\int_{0}^{12} 144 - x^{2} d x

\int_{0}^{5} \frac{1}{25 + t ^{2}} d t

\int_{2}^{3} e^{2 - x} d x

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