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

The integral from 0 to x^2 of x+y is x^3+(x^4)/2

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integral from 0 to x^2 of x+y

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

x^{3} + \frac{x ^{4}}{2}

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{x^{2}} x d y + \int_{0}^{x^{2}} y d y

\int_{0}^{x^{2}} x d y = x^{3}

\int_{0}^{x^{2}} y d y = \frac{x ^{4}}{2}

= x^{3} + \frac{x ^{4}}{2}

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What is the integral from 0 to x^2 of x+y ?
The integral from 0 to x^2 of x+y is x^3+(x^4)/2