What is the integral from 0 to 1 of x^2y ?

The integral from 0 to 1 of x^2y is y/3

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integral from 0 to 1 of x^2y

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

\frac{y}{3}

Solution steps

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

Take the constant out:

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

= y \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{1}

= y [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= y \frac{1}{3}

Simplify

= \frac{y}{3}

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

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

\int_{1}^{2} \frac{5 - x}{8} d x

\int_{- π}^{π} (x + 1)^{2} sin (x) d x

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

What is the integral from 0 to 1 of x^2y ?
The integral from 0 to 1 of x^2y is y/3