What is the integral from 2 to 4 of (sqrt(25-x^2))^2 ?

The integral from 2 to 4 of (sqrt(25-x^2))^2 is 94/3

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integral from 2 to 4 of (sqrt(25-x^2))^2

\int_{2}^{4} (25 - x^{2})^{2} d x

\frac{94}{3}

Decimal Notation

31.33333 \dots

Solution steps

\int_{2}^{4} (25 - x^{2})^{2} d x

Simplify

(25 - x^{2})^{2} : 25 - x^{2}

= \int_{2}^{4} 25 - 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}^{4} 25 d x - \int_{2}^{4} x^{2} d x

\int_{2}^{4} 25 d x = 50

\int_{2}^{4} x^{2} d x = \frac{56}{3}

= 50 - \frac{56}{3}

Simplify

50 - \frac{56}{3} : \frac{94}{3}

= \frac{94}{3}

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What is the integral from 2 to 4 of (sqrt(25-x^2))^2 ?
The integral from 2 to 4 of (sqrt(25-x^2))^2 is 94/3