Exam

JEE Main

Year

2025

Date

29 January

Shift

Morning Shift

Subject

Mathematics

Chapter

Area Under Curves

JEE Main 2025 · 29 January · Morning Shift · Mathematics · Area Under Curves

Let the area of the region (\ (x, y): 2 y ≤ x^2+3, y+|x| ≤ 3, y...

Let the area of the region (\left\{(x, y): 2 y \leq x^2+3, y+|x| \leq 3, y \geqslant|x-1|\right\}) be A. Then 6 A is equal to :

Step-by-step solution

$A \Rightarrow$ Rectangle ABDE - Area of region EDC $$\begin{aligned} & A \Rightarrow 4-2 \int_0^1(3-x)-\left(\frac{x^2+3}{2}\right) d x \\ & A \Rightarrow 4-2\left\{3 x-\frac{x^2}{2}-\frac{x^3}{6}-\frac{3}{2} x\right\}_0^1 \\ & A \Rightarrow 4-2\left\{3-\frac{1}{2}-\frac{1}{6}-\frac{3}{2}\right\}=\frac{7}{3} \end{aligned}$$ So $6 \mathrm{~A}=14$