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JEE Main 202228 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
28 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2022 · 28 June · Evening Shift · Mathematics · Area Under Curves

The area of the bounded region enclosed by the curve y = 3 - |x -...

The area of the bounded region enclosed by the curve y=3−∣x−12∣−∣x+1∣y = 3 - \left|x - \dfrac{1}{2}\right| - \left|x + 1\right| and the xx-axis isThe area of the bounded region enclosed by the curve y = 3 - |x - (1)/(2)| - |x + 1| and the x -axis is

Options

  1. A94\dfrac{9}{4}
  2. B4516\dfrac{45}{16}
  3. C278\dfrac{27}{8}
  4. D6316\dfrac{63}{16}

Correct answer

C. 278\dfrac{27}{8}

Step-by-step solution

Plotting the graph of the function y=3−∣x+1∣−∣x−12∣y = 3 - \left|x + 1\right| - \left|x - \dfrac{1}{2}\right| and xx-axis, we get

The area of the bounded region enclosed by the curve y = 3 - |x - (1)/(2)| - |x + 1| and the x -axis is

Now applying the formula of area of trapezium which is 12×height×(sum of parallel sides)\dfrac{1}{2} \times \text{height} \times \left(\text{sum of parallel sides}\right) we get,

Required area of Trap(ABCD)=12×32×(3+32)=278Trap\left(ABCD\right) = \dfrac{1}{2} \times \dfrac{3}{2} \times \left(3 + \dfrac{3}{2}\right) = \dfrac{27}{8}

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