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

Lösung

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

\frac{500}{3}

Dezimale

166.66666 \dots

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summenregel an:

\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}

Vereinfache

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

= \frac{500}{3}

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

d er i v a t i v e (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})

p a r i t y \frac{sin ^{5} ( e ^{2 x} )}{cos ( 7 ^{6 x} )}