Question

Curve C is defined by the equation $y=\sqrt{(9-x^2)}$ with $x\ge 0$. The area bounded by curve C, the x-axis and the y-axis is

• A. $\frac{\pi }{4}$
• B. $\frac{9\pi }{4}$
• C. $\frac{9\pi }{2}$
• D. $9Pi$
• E. $\frac{81\pi }{4}$

Answer 1

The correct option is B $\frac{9\pi }{4}$

$y=\sqrt{9-x^2}$

at $y=0$ ,$x=3,-3$

But given $x_{-}^{>}0$

hence $A={\int }_0^3(\sqrt{9-x^2})$

$A=(\frac{x\sqrt{9-x^2}}{2}+\frac{9{\sin }^{-1}\left(\frac{x}{3}\right)}{2}){|}_0^3$

apply lower and upper limit, we will get

$A=\frac{9\pi }{4}$