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  • Choose the correct answer in the following .Area lying in the first quadrant and bounded by the circle x^2 + y^2 = 4 and the lines x = 0 and x = 2 is (A) π (B) 2 π (C) 3 π (D) 4 π

Q : 12        Choose the correct answer in the following. 

                  Area lying in the first quadrant and bounded by the circle \small x^2+y^2=4  and the lines \small x=0 and                    \small x=2  is

                   \small (A)\hspace{1mm}\pi           \small (B)\hspace{1mm}\frac{\pi }{2}           \small (C)\hspace{1mm}\frac{\pi }{3}        \small (D)\hspace{1mm}\frac{\pi }{4}
                   

Answers (1)

best_answer

The correct answer is A
The area bounded by circle C(0,0,4) and the line x=2 is

The required area = area of OAB
                              \int^2_0ydx = \int^2_0\sqrt{4-x^2}dx
                                                \\=[\frac{x}{2}\sqrt{4-x^2}+\frac{4}{2}\sin^{-1}\frac{x}{2}]^2_0\\ =2(\pi/2)\\ =\pi

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manish

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