What is the integral from-4 to 4 of x^2+y^2 ?

The integral from-4 to 4 of x^2+y^2 is 8y^2+128/3

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integral from-4 to 4 of x^2+y^2

\int_{- 4}^{4} x^{2} + y^{2} d x

8 y^{2} + \frac{128}{3}

Solution steps

\int_{- 4}^{4} 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_{- 4}^{4} y^{2} d x + \int_{- 4}^{4} x^{2} d x

\int_{- 4}^{4} y^{2} d x = 8 y^{2}

\int_{- 4}^{4} x^{2} d x = \frac{128}{3}

= 8 y^{2} + \frac{128}{3}

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

\int_{0}^{1} x^{2} (x^{\frac{2}{3}}) d x

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

\int_{0}^{\frac{π}{6}} 2 cos (x) d x

\int_{0}^{4} 4 x + 5 d x

What is the integral from-4 to 4 of x^2+y^2 ?
The integral from-4 to 4 of x^2+y^2 is 8y^2+128/3