Question

${\int }_0^3(9-x^2{)}^{3/2}d{x}_{=}$

• A. $\frac{243\pi }{16}$
• B. $\frac{\pi }{16}$
• C. $\frac{-243{\pi }^2}{15}$
• D. $\frac{81\pi }{16}$

Answer 1

The correct option is A $\frac{243\pi }{16}$

$x=3sin\theta$
$dx=3cos\theta \cdot d\theta$
${\int }_0^{\frac{\pi }{2}}(3cos\theta {)}^{3}d\theta$
$27{\int }_0^{\frac{\pi }{2}}co{s}^4\theta d\theta$
$27{(\frac{3}{4}\cdot \frac{1}{2}\cdot \frac{\pi }{2})}^3$
$\frac{243}{16}\pi$