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

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

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integral from-sqrt(2) to sqrt(2 of)2-x^2

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

42 - \frac{4 2}{3}

Decimal

3.77123 \dots

Solution steps

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

\int_{- 2}^{2} 2 d x = 42

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

= 42 - \frac{4 2}{3}

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