What is the integral from 2 to 4 of 2x-(x^2)/2 ?

The integral from 2 to 4 of 2x-(x^2)/2 is 8/3

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integral from 2 to 4 of 2x-(x^2)/2

\int_{2}^{4} 2 x - \frac{x ^{2}}{2} d x

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

\int_{2}^{4} 2 x - \frac{x ^{2}}{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_{2}^{4} 2 x d x - \int_{2}^{4} \frac{x ^{2}}{2} d x

\int_{2}^{4} 2 x d x = 12

\int_{2}^{4} \frac{x ^{2}}{2} d x = \frac{28}{3}

= 12 - \frac{28}{3}

Simplify

12 - \frac{28}{3} : \frac{8}{3}

= \frac{8}{3}

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What is the integral from 2 to 4 of 2x-(x^2)/2 ?
The integral from 2 to 4 of 2x-(x^2)/2 is 8/3