What is the integral from y to 2y of (10+2x^2+2y^2) ?

The integral from y to 2y of (10+2x^2+2y^2) is 10y+2y^3+(14y^3)/3

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integral from y to 2y of (10+2x^2+2y^2)

\int_{y}^{2 y} (10 + 2 x^{2} + 2 y^{2}) d x

10 y + 2 y^{3} + \frac{14 y ^{3}}{3}

Solution steps

\int_{y}^{2 y} 10 + 2 x^{2} + 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_{y}^{2 y} 10 d x + \int_{y}^{2 y} 2 y^{2} d x + \int_{y}^{2 y} 2 x^{2} d x

\int_{y}^{2 y} 10 d x = 10 y

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

\int_{y}^{2 y} 2 x^{2} d x = \frac{14 y ^{3}}{3}

= 10 y + 2 y^{3} + \frac{14 y ^{3}}{3}

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What is the integral from y to 2y of (10+2x^2+2y^2) ?
The integral from y to 2y of (10+2x^2+2y^2) is 10y+2y^3+(14y^3)/3