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JEE Main 20236 AprilEvening Shift

Exam: JEE Main
Year: 2023
Date: 6 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2023 · 6 April · Evening Shift · Mathematics · Area Under Curves

The area bounded by the curves y = |x - 1| + |x - 2| and y = 3 is...

The area bounded by the curves $y = \left|x - 1\right| + \left|x - 2\right|$ and $y = 3$ is equal to

The area bounded by the curves y = |x - 1| + |x - 2| and y = 3 is equal to

Options

A $4$
B $6$
C $3$
D $5$

Correct answer

A. $4$

Step-by-step solution

Given:
$y = f\left(x\right) = \left|x - 1\right| + \left|x - 2\right|$
$⇒ f\left(x\right) = \left\{$ $\begin{array}{ll}3 - 2x: x < 11; 1 \le x < 2 \\ 2x - 3; x \ge 2\end{array}$ $\right)</p><p>Let us draw diagram of$ y = f\left(x\right) \text{ and } y = 3 $we get,</p><p><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/fffa10be-f7d1-4bd4-a9cf-a20cf2f6aaeb-image.png" style="width: 375px; height: 191px;" /></p><p>Required area is the area of trapezium which is</p><p>Area$ = \dfrac{1}{2}\left[1 + 3\right] \times 2 $</p><p>$ = 4 sq. units

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