Exam

JEE Main

Year

2019

Date

8 April

Shift

Morning Shift

Subject

Mathematics

Chapter

Area Under Curves

JEE Main 2019 · 8 April · Morning Shift · Mathematics · Area Under Curves

The area (in sq. units) of the region A = \ (x, y) ∈ R × R0 ≤ x ≤...

The area (in sq. units) of the region $A = \left\{\left(x, y\right) \in R \times R0 \le x \le 3, 0 \le y \le 4, y \le {x}^{2} + 3x\right\}$ is

Step-by-step solution

The area of the region $OCD$ is
$= \mathop{∫}_{0}^{1}\left[4 - \left({x}^{2} + 3x\right)\right]dx = {\left[4x - \dfrac{{x}^{3}}{3} - \dfrac{3{x}^{2}}{2}\right]}_{0}^{1} = 4 - \dfrac{1}{3} - \dfrac{3}{2} = \dfrac{13}{6}$
So, the area of the given region $OABC$ is
= Area of $OABD$ $-$ Area of $OCD$
$= 3 \times 4 - \dfrac{13}{6}$
$= \dfrac{59}{6}$