What is the integral from-5 to 5 of (sqrt(25-x^2))^2 ?

The integral from-5 to 5 of (sqrt(25-x^2))^2 is 500/3

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integral from-5 to 5 of (sqrt(25-x^2))^2

\int_{- 5}^{5} (25 - x^{2})^{2} d x

\frac{500}{3}

Decimal Notation

166.66666 \dots

Solution steps

\int_{- 5}^{5} (25 - x^{2})^{2} d x

Simplify

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

= \int_{- 5}^{5} 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_{- 5}^{5} 25 d x - \int_{- 5}^{5} x^{2} d x

\int_{- 5}^{5} 25 d x = 250

\int_{- 5}^{5} x^{2} d x = \frac{250}{3}

= 250 - \frac{250}{3}

Simplify

250 - \frac{250}{3} : \frac{500}{3}

= \frac{500}{3}

\frac{d}{d x} (cos (5 x) \cdot 5)

(2 e^{x})^{2} - (10 e^{x})

\int \frac{1}{7 x ^{3}} d x

\frac{d}{d x} ((7 x + x^{2} + 3)^{6})

\frac{sin ^{5} ( e ^{2 x} )}{cos ( 7 ^{6 x} )}

What is the integral from-5 to 5 of (sqrt(25-x^2))^2 ?
The integral from-5 to 5 of (sqrt(25-x^2))^2 is 500/3