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

The integral from x to 2x of (x^2+y^2) is x^3+(7x^3)/3

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integral from x to 2x of (x^2+y^2)

\int_{x}^{2 x} (x^{2} + y^{2}) d y

x^{3} + \frac{7 x ^{3}}{3}

Solution steps

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

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

\int_{x}^{2 x} y^{2} d y = \frac{7 x ^{3}}{3}

= x^{3} + \frac{7 x ^{3}}{3}

What is the integral from x to 2x of (x^2+y^2) ?
The integral from x to 2x of (x^2+y^2) is x^3+(7x^3)/3