What is the integral from 0 to 1 of 6x^2y ?

The integral from 0 to 1 of 6x^2y is 2y

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integral from 0 to 1 of 6x^2y

\int_{0}^{1} 6 x^{2} y d x

2 y

Solution steps

\int_{0}^{1} 6 x^{2} y d x

Take the constant out:

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

= 6 y \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

= 6 y [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= 6 y \frac{1}{3}

Simplify

= 2 y

What is the integral from 0 to 1 of 6x^2y ?
The integral from 0 to 1 of 6x^2y is 2y