What is the integral from y to 1 of 10x^2y ?

The integral from y to 1 of 10x^2y is (10y(1-y^3))/3

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integral from y to 1 of 10x^2y

\int_{y}^{1} 10 x^{2} y d x

\frac{10 y ( 1 - y ^{3} )}{3}

Solution steps

\int_{y}^{1} 10 x^{2} y d x

Take the constant out:

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

= 10 y \cdot \int_{y}^{1} x^{2} d x

Apply the Power Rule

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

= 10 y [\frac{x ^{3}}{3}]_{y}^{1}

Compute the boundaries:

\frac{1}{3} - \frac{y ^{3}}{3}

= 10 y (\frac{1}{3} - \frac{y ^{3}}{3})

Simplify

= \frac{10 y ( 1 - y ^{3} )}{3}

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What is the integral from y to 1 of 10x^2y ?
The integral from y to 1 of 10x^2y is (10y(1-y^3))/3