What is the integral from-2 to 2 of 1-(x^2)/4 ?

The integral from-2 to 2 of 1-(x^2)/4 is 8/3

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integral from-2 to 2 of 1-(x^2)/4

\int_{- 2}^{2} 1 - \frac{x ^{2}}{4} d x

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{- 2}^{2} 1 - \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_{- 2}^{2} 1 d x - \int_{- 2}^{2} \frac{x ^{2}}{4} d x

\int_{- 2}^{2} 1 d x = 4

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

= 4 - \frac{4}{3}

Simplify

4 - \frac{4}{3} : \frac{8}{3}

= \frac{8}{3}

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\int_{0}^{1} 3.6 x^{3} - 2.4 x^{4} d x

What is the integral from-2 to 2 of 1-(x^2)/4 ?
The integral from-2 to 2 of 1-(x^2)/4 is 8/3