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QJEEM22Ma24ff: JEE Main 2022 Mathematics - Class 12 JEEM22Ma24ff Solution: The area of the bounded region enclosed by the curve and the…

The area of the bounded region enclosed by the curve

y=3−∣x−12∣−∣x+1∣y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1| and the x-axis is :

Multiple Choice Options

  • A 94{9 \over 4}
  • B 4516{45 \over 16}
  • C 278{27 \over 8}
  • D 6316{63 \over 16}

Step-by-Step Verified Solution

JEE Main 2022 (Online) 28th June Evening Shift Mathematics - Area Under The Curves Question 78 English Explanation
y={2x−72amp;xlt;−132amp;−1≤x≤1252−2xamp;xgt;12y=\left\{\begin{array}{cc}2 x-\frac{7}{2} & x<-1 \\\\\frac{3}{2} & -1 \leq x \leq \frac{1}{2} \\\\\frac{5}{2}-2 x & x>\frac{1}{2}\end{array}\right.

y=3−∣x−12∣−∣x+1∣y=3-\left|x-\frac{1}{2}\right|-|x+1|

Area of shaded region (required area)

=12(3+32)⋅32=278=\frac{1}{2}\left(3+\frac{3}{2}\right) \cdot \frac{3}{2}=\frac{27}{8}

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