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JEE Main 201322 AprilOnline

Exam: JEE Main
Year: 2013
Date: 22 April
Mode: Online
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2013 · 22 April · Online · Mathematics · Area Under Curves

The area of the region (in sq. units), in the first quadrant...

The area of the region (in sq. units), in the first quadrant bounded by the parabola

y=9 x^2

and the lines

x=0, y=1

and

y=4

, is :

Options

A $7 / 9$
B $14 / 3$
C $7 / 3$
D $14 / 9$

Correct answer

D. $14 / 9$

Step-by-step solution

\begin{aligned}& \text{ Required area }=\int_{y=1}^4 \sqrt{\frac{y}{9}}d y \\ & =\frac{1}{3} \int_{y=1}^4 y^{1 / 2} d y=\frac{1}{3} \times\left.\frac{2}{3}\left(y^{3 / 2}\right)\right|_1 ^4 \\ & =\frac{2}{9}\left[\left(4^{1 / 2}\right)^3-\left(1^{1 / 2}\right)^3\right]=\frac{2}{9}[8-1] \end{aligned}

=

\frac{2}{9} \times

7=

\frac{14}{9} \text{ sq. units. }

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