Verified Solution • 2025–26 Session moderate

QJEEM19Ma1eb8: JEE Main 2019 Mathematics - Class 12 JEEM19Ma1eb8 Solution: The area (in sq. units) of the region A = { (x, y) R ×…

The area (in sq. units) of the region
A = { (x, y) ∈\in R × R|  0 ≤\le x ≤\le 3, 0 ≤\le y ≤\le 4, y ≤\le x2 + 3x} is :

Multiple Choice Options

  • A 596{{59} \over 6}
  • B 263{{26} \over 3}
  • C 8
  • D 536{{53} \over 6}

Step-by-Step Verified Solution

JEE Main 2019 (Online) 8th April Morning Slot Mathematics - Area Under The Curves Question 115 English Explanation

When y = 4 then,

x2 + 3x = 4

⇒\Rightarrow x2 + 3x - 4 = 0

⇒\Rightarrow x2 + 4x - x - 4 = 0

⇒\Rightarrow x(x + 4) - (x + 4) = 0

⇒\Rightarrow (x + 4)(x - 1) = 0

⇒\Rightarrow x = 1, - 4

As 0 ≤\le x ≤\le 3,

so possible value of x = 1.

∴\therefore y = x2 + 3x parabola cut the line y = 4 at x = 1.

Required area

= ∫01(x2+3x)dx\int\limits_0^1 {\left( {{x^2} + 3x} \right)} dx + 2 ×\times 4

= [x33+3(x22)]01\left[ {{{{x^3}} \over 3} + 3\left( {{{{x^2}} \over 2}} \right)} \right]_0^1 + 8

= (13+32){\left( {{1 \over 3} + {3 \over 2}} \right)} + 8

= 116+8{{11} \over 6} + 8

= 596{{59} \over 6}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring