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

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

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integral from 1 to 2 of x^2y

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

\frac{3 x ^{2}}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{1}^{2}

= x^{2} [\frac{y ^{2}}{2}]_{1}^{2}

Compute the boundaries:

\frac{3}{2}

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

Simplify

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

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