The region R is bounded by the circle and the vertical line

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

The region R is bounded by the circle x2+y2=4x^{2}+y^{2}=4 and the vertical line x=1x=1. Which of the following definite integrals represents the area of R? (a) ∫−22(4−y2−1) dy\displaystyle \int_{-2}^{2}\left(\sqrt{4-y^{2}}-1\right)\,dy (b) 2∫034−y2 dy\displaystyle 2\int_{0}^{\sqrt{3}}\sqrt{4-y^{2}}\,dy (c) ∫−33(4−y2−1) dy\displaystyle \int_{-\sqrt{3}}^{\sqrt{3}}\bigl(\sqrt{4-y^{2}}-1\bigr)\,dy (d) ∫03(4−y2−1) dy\displaystyle \int_{0}^{\sqrt{3}}\left(\sqrt{4-y^{2}}-1\right)\,dy

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