What is the integral from 0 to 1 of 30xy ?

The integral from 0 to 1 of 30xy is 15x

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integral from 0 to 1 of 30xy

\int_{0}^{1} 30 x y d y

15 x

Solution steps

\int_{0}^{1} 30 x y d y

Take the constant out:

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

= 30 x \cdot \int_{0}^{1} y d y

Apply the Power Rule

= 30 x [\frac{y ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= 30 x \frac{1}{2}

Simplify

= 15 x

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\int_{0}^{10} \frac{1}{2} x d x

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What is the integral from 0 to 1 of 30xy ?
The integral from 0 to 1 of 30xy is 15x