Q. The area of the plane region bounded by the curve $x = y^{2} - 2$ and the line $y = - x$ is (in square units)
A) $\frac{13}{3}$
B) $\frac{2}{5}$
C) $\frac{9}{2}$
D) $\frac{5}{2}$
Explanation
(c)
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Required area
$= 2\int_{- 2}^{- 1}\sqrt{x + 2}dx + \int_{- 1}^{2}{( - x + \sqrt{x + 2}})dx$
$= \frac{4}{3}\lbrack(x + 2)^{3/2}\rbrack_{- 2}^{- 1} + \left\lbrack \frac{- x^{2}}{2} + \frac{2}{3}(x + 2)^{3/2} \right\rbrack_{- 1}^{2}$
$= \frac{9}{2}\ sq\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.