What is the integral from 0 to k of (2kx-x^2) ?

The integral from 0 to k of (2kx-x^2) is k^3-(k^3)/3

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integral from 0 to k of (2kx-x^2)

\int_{0}^{k} (2 k x - x^{2}) d x

k^{3} - \frac{k ^{3}}{3}

Solution steps

\int_{0}^{k} 2 k x - x^{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}^{k} 2 k x d x - \int_{0}^{k} x^{2} d x

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

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

= k^{3} - \frac{k ^{3}}{3}

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What is the integral from 0 to k of (2kx-x^2) ?
The integral from 0 to k of (2kx-x^2) is k^3-(k^3)/3