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QJEEM23Ma5cdb: JEE Main 2023 Mathematics - Class 12 JEEM23Ma5cdb Solution: The area of the region is

The area of the region {(x,y):x2≤y≤∣x2−4∣,y≥1}\left\{(x, y): x^{2} \leq y \leq\left|x^{2}-4\right|, y \geq 1\right\} is

Multiple Choice Options

  • A 43(42+1)\frac{4}{3}(4 \sqrt{2}+1)
  • B 34(42+1)\frac{3}{4}(4 \sqrt{2}+1)
  • C 43(42−1)\frac{4}{3}(4 \sqrt{2}-1)
  • D 34(42−1)\frac{3}{4}(4 \sqrt{2}-1)

Step-by-Step Verified Solution

JEE Main 2023 (Online) 13th April Evening Shift Mathematics - Area Under The Curves Question 43 English Explanation

amp; Required area =2[∫12ydy+∫424−ydy]amp;=2[y3/232]12−2(4−y)3/23]24]amp;=43(42−1)\begin{aligned}& \text { Required area }=2\left[\int_1^2 \sqrt{y} d y+\int_4^2 \sqrt{4-y} d y\right] \\\\& \left.\left.=2\left[\frac{y^{3 / 2}}{\frac{3}{2}}\right]_1^2-\frac{2(4-y)^{3 / 2}}{3}\right]_2^4\right] \\\\& =\frac{4}{3}(4 \sqrt{2}-1)\end{aligned}

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