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

The integral from 1 to 3 of x^2y is x^2*4

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integral from 1 to 3 of x^2y

\int_{1}^{3} x^{2} y d y

x^{2} \cdot 4

Solution steps

\int_{1}^{3} 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}^{3} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{1}^{3}

= x^{2} [\frac{y ^{2}}{2}]_{1}^{3}

Compute the boundaries:

4

= x^{2} \cdot 4

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What is the integral from 1 to 3 of x^2y ?
The integral from 1 to 3 of x^2y is x^2*4