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JEE Main 20208 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
8 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2020 · 8 January · Evening Shift · Mathematics · Area Under Curves

The area (in sq. units) of the region \ (x, y) ∈ R ^ 2 : x ^ 2 ≤ y...

The area (in sq. units) of the region {(x,y)∈R2:x2≤y≤3−2x}\left\{\left(x, y\right) \in {R}^{2}: {x}^{2} \le y \le 3 - 2x\right\}, is.The area (in sq. units) of the region \ (x, y) ∈ R ^ 2 : x ^ 2 ≤ y ≤ 3 - 2x\ , is.

Options

  1. A323\dfrac{32}{3}
  2. B343\dfrac{34}{3}
  3. C293\dfrac{29}{3}
  4. D313\dfrac{31}{3}

Correct answer

A. 323\dfrac{32}{3}

Step-by-step solution

Point of intersection of y=x2 and y=−2x+3y = {x}^{2} \text{ and } y = - 2x + 3, is obtained by x2+2x−3=0{x}^{2} + 2x - 3 = 0⟹x=−3,1⟹ x = - 3, 1.

The area (in sq. units) of the region \ (x, y) ∈ R ^ 2 : x ^ 2 ≤ y ≤ 3 - 2x\ , is.

So, area of the required region is

∫−31((3−2x)−x2)dx{∫}_{- 3}^{1}\left(\left(3 - 2x\right) - {x}^{2}\right) d x

=[3x−x2−x33]−31=323= {\left[3x - {x}^{2} - \dfrac{{x}^{3}}{3}\right]}_{- 3}^{1} = \dfrac{32}{3}.

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