Verified Solution • 2025–26 Session moderate

QJEEM24Mad22c: JEE Main 2024 Mathematics - Class 12 JEEM24Mad22c Solution: The area (in sq. units) of the region described by is

The area (in sq. units) of the region described by {(x,y):y2≤2x, and y≥4x−1}\left\{(x, y): y^2 \leq 2 x \text {, and } y \geq 4 x-1\right\} is

Multiple Choice Options

  • A 932\frac{9}{32}
  • B 1112\frac{11}{12}
  • C 89\frac{8}{9}
  • D 1132\frac{11}{32}

Step-by-Step Verified Solution

 Area =∫−121(y+14−y22)dy

JEE Main 2024 (Online) 4th April Evening Shift Mathematics - Area Under The Curves Question 17 English Explanation

amp;=[y28+y4−y36]−121amp;=(18+14−16)−(132−18+148)amp;=524+796amp;=2796amp;=932\begin{aligned}& =\left[\frac{y^2}{8}+\frac{y}{4}-\frac{y^3}{6}\right]_{-\frac{1}{2}}^1 \\& =\left(\frac{1}{8}+\frac{1}{4}-\frac{1}{6}\right)-\left(\frac{1}{32}-\frac{1}{8}+\frac{1}{48}\right) \\& =\frac{5}{24}+\frac{7}{96} \\& =\frac{27}{96} \\& =\frac{9}{32}\end{aligned}

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