The area of the region : [R = (x,y):5x^2 y 2x^2 + 9 ] is :

Question

The area of the region : $$R = \{ (x,y):5{x^2} \le y \le 2{x^2} + 9\} $$ is :

Accepted Answer

Required area

$$ = 2\int\limits_0^{\sqrt 3 } {\left( {2{x^2} + 9 - 5{x^2}} \right)} dx$$

$$ = 2\int\limits_0^{\sqrt 3 } {\left( {9 - 3{x^2}} \right)dx} $$

$$ = 2|\,9x - {x^3}\,|_0^{\sqrt 3 } = 12\sqrt 3 $$

Solutions · 1