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

The integral from 0 to 2 of x^2+y^2 is 2y^2+8/3

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

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

2 y^{2} + \frac{8}{3}

Solution steps

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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 2 y^{2} + \frac{8}{3}

\int_{- 2}^{1} x^{- 5} d x

\int_{0}^{7} 3 x d x

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

\int_{1}^{2} x^{2} - 1 d x

\int_{- 3}^{3} 5 - 9 - x^{2} d x

What is the integral from 0 to 2 of x^2+y^2 ?
The integral from 0 to 2 of x^2+y^2 is 2y^2+8/3