JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q9

MathematicsSingle correct+4 / -1Question 9 of 90

The area of the bounded region enclosed by the curve $y=3-\left|x-\dfrac12\right|-|x+1|$ and the $x$ -axis is :

\dfrac94

\dfrac{45}{16}

\dfrac{27}8

\dfrac{63}{16}

Answer and worked solution

Official answer: C

Graph. $y=\frac32$ on $\left[-1,\frac12\right]$ , falling to 0 at $x=\frac54$ on the right and at $x=-\frac74$ on the left.

Trapezium. $\frac12\left(\frac32+3\right)\cdot\frac32=\frac{27}8$ .

(C)

Topics:Area under a curve Inequalities and modulus

JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 9