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

The integral from 1 to 3 of 3x^2y is 26y

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integral from 1 to 3 of 3x^2y

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

26 y

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{26}{3}

= 3 y \frac{26}{3}

Simplify

= 26 y

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What is the integral from 1 to 3 of 3x^2y ?
The integral from 1 to 3 of 3x^2y is 26y