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

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

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integral from 0 to sqrt(2 of)(2-x^2)

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

22 - \frac{2 2}{3}

Decimal

1.88561 \dots

Solution steps

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

\int_{0}^{2} 2 d x = 22

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

= 22 - \frac{2 2}{3}

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