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JEE Main 20257 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
7 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2025 · 7 April · Evening Shift · Mathematics · Area Under Curves

If the area of the region \ (x, y): 1+x^2 ≤ y ≤ \ x+7,11-3 x\ \ is...

If the area of the region {(x,y):1+x2≤y≤min⁡{x+7,11−3x}}\left\{(\mathrm{x}, \mathrm{y}): 1+\mathrm{x}^2 \leq \mathrm{y} \leq \min \{\mathrm{x}+7,11-3 \mathrm{x}\}\right\} is A , then 3 A is equal to

Options

  1. A50
  2. B49
  3. C46
  4. D47

Correct answer

A. 50

Step-by-step solution

A=∫−21(x+7−x2−1)dx+∫12(11+3x−x2−1)dx=[x22+6x−x33]−21+[10x−3x22−x33]12=503⇒3A=50 Option (1) \begin{aligned} & A=\int_{-2}^1\left(x+7-x^2-1\right) d x+\int_1^2\left(11+3 x-x^2-1\right) d x \\ & =\left[\frac{x^2}{2}+6 x-\frac{x^3}{3}\right]_{-2}^1+\left[10 x-\frac{3 x^2}{2}-\frac{x^3}{3}\right]_1^2 \\ & =\frac{50}{3} \Rightarrow 3 A=50 \quad \text{ Option (1) }\end{aligned}
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