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JEE Main 201815 AprilMorning ShiftOnline

Exam: JEE Main
Year: 2018
Date: 15 April
Shift: Morning Shift
Mode: Online
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2018 · 15 April · Morning Shift · Online · Mathematics · Area Under Curves

The area (in sq. units) of the region \ x ∈ R: x ≥ 0, y ≥ 0, y ≥...

The area (in sq. units) of the region

\{x \in R: x \geq 0, y \geq 0, y \geq x-2

and

y \leq \sqrt{x}\}

, is $The area (in sq. units) of the region \ x ∈ R: x ≥ 0, y ≥ 0, y ≥ x-2 and y ≤ x \ , is$ $The area (in sq. units) of the region \ x ∈ R: x ≥ 0, y ≥ 0, y ≥ x-2 and y ≤ x \ , is$

Options

A $\frac{13}{3}$
B $\frac{10}{3}$
C $\frac{5}{3}$
D $\frac{8}{3}$

Correct answer

B. $\frac{10}{3}$

Step-by-step solution

The intersection point of

y=x-2

and

y=\sqrt{x}

is

(4,2)

. The required area =\int_0^4

\sqrt{x}

d x-

\frac{1}{2} \times

2

\times

2=

\frac{16}{3}-

2=

\frac{10}{3}

$The area (in sq. units) of the region \ x ∈ R: x ≥ 0, y ≥ 0, y ≥ x-2 and y ≤ x \ , is$

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