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

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

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integral from 0 to y of x^2+y^2

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

y^{3} + \frac{y ^{3}}{3}

Solution steps

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

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

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

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

= y^{3} + \frac{y ^{3}}{3}

\int_{0}^{x} 4 + t^{6} d x

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