What is the integral from 21 to 32 of k(x^2+y^2) ?

The integral from 21 to 32 of k(x^2+y^2) is k(11x^2+23507/3)

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integral from 21 to 32 of k(x^2+y^2)

\int_{21}^{32} k (x^{2} + y^{2}) d y

k (11 x^{2} + \frac{23507}{3})

Solution steps

\int_{21}^{32} k (x^{2} + y^{2}) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= k \cdot \int_{21}^{32} 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

= k (\int_{21}^{32} x^{2} d y + \int_{21}^{32} y^{2} d y)

\int_{21}^{32} x^{2} d y = 11 x^{2}

\int_{21}^{32} y^{2} d y = \frac{23507}{3}

= k (11 x^{2} + \frac{23507}{3})

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What is the integral from 21 to 32 of k(x^2+y^2) ?
The integral from 21 to 32 of k(x^2+y^2) is k(11x^2+23507/3)