What is the integral from 0 to x^2 of 10y ?

The integral from 0 to x^2 of 10y is 5x^4

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integral from 0 to x^2 of 10y

\int_{0}^{x^{2}} 10 y d y

5 x^{4}

Solution steps

\int_{0}^{x^{2}} 10 y d y

Take the constant out:

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

= 10 \cdot \int_{0}^{x^{2}} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{x^{2}}

= 10 [\frac{y ^{2}}{2}]_{0}^{x^{2}}

Compute the boundaries:

\frac{x ^{4}}{2}

= 10 \cdot \frac{x ^{4}}{2}

Simplify

= 5 x^{4}

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What is the integral from 0 to x^2 of 10y ?
The integral from 0 to x^2 of 10y is 5x^4