What is the integral from 0 to 2 of x^2-(x^2)/4 ?

The integral from 0 to 2 of x^2-(x^2)/4 is 2

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integral from 0 to 2 of x^2-(x^2)/4

\int_{0}^{2} x^{2} - \frac{x ^{2}}{4} d x

2

Solution steps

\int_{0}^{2} x^{2} - \frac{x ^{2}}{4} 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}^{2} x^{2} d x - \int_{0}^{2} \frac{x ^{2}}{4} d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} \frac{x ^{2}}{4} d x = \frac{2}{3}

= \frac{8}{3} - \frac{2}{3}

Simplify

\frac{8}{3} - \frac{2}{3} : 2

= 2

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What is the integral from 0 to 2 of x^2-(x^2)/4 ?
The integral from 0 to 2 of x^2-(x^2)/4 is 2