QJEEM15Ma2560: JEE Main 2015 Mathematics - Class 12 JEEM15Ma2560 Solution: The area (in sq. units) of the region described by { ( x , y )…

Question

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The area (in sq. units) of the region described by

{(x, y) : y^{2} \leq 2 x

and

y \geq 4 x - 1}

is :

Accepted Answer

Required area

JEE Main 2015 (Offline) Mathematics - Area Under The Curves Question 130 English Explanation

=

Area of

A B C D

-

a r

(A B O C D)

= \frac{1}{4} {[\frac{y^{2}}{2} + y]}_{- 1 / 2}^{1} - \frac{1}{2} {[\frac{y^{3}}{3}]}_{- 1}^{1}

= \frac{1}{4} [\frac{3}{2} + \frac{3}{8}] - \frac{9}{48}

= \frac{15}{32} - \frac{9}{48} = \frac{27}{96} = \frac{9}{32}

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