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QJEEM21Ma7678: JEE Main 2021 Mathematics - Class 12 JEEM21Ma7678 Solution: The area (in sq. units) of the region, given by the set is :

The area (in sq. units) of the region, given by the set

\{ (x,y) \in R \times R|x \ge 0,2{x^2} \le y \le 4 - 2x\}

is :

Step-by-Step Verified Solution

Required area =

\left. {\int\limits_0^1 {\left( {4 - 2x - 2{x^2}} \right)dx = 4x - {x^2} - {{2{x^3}} \over 3}} } \right|_0^1

= 4 - 1 - {2 \over 3} = {7 \over 3}