Question

Smaller area enclosed by the circle x2+y2=4 and the line x+y=2 is

• A. 2(π-2)
• B. π-2
• C. 2π-1
• D. 2(π+2)

Answer 1

Answer: (B)

π-2

Answer 2

The smaller area enclosed by the circle,x2+y2=4,and the line,x+y=2,is

represented by the shaded area ACBA as

It can be observed that,

Area ACBA=Area OACBO-Area(ΔOAB)=

\int_{1}^{2} \sqrt{4-x^2} \,dx$$$$-\int_{0}^{2} (2-x) \,dx

=[\frac{x}{2}$$\sqrt{4-x^2}+$\frac{4}{2}$sin-1$\frac{x}{2}$]20-[2x-$\frac{x^2}{2}$]20

=[2.π/2]-[4-2]

=(π-2)units.

Thus,the correct answer is B.