The area of the region: R= (x, y): 5 x2 ≤ y ≤ 2 x2+9 is

Question

The area of the region: R= (x, y): 5 x2 ≤ y ≤ 2 x2+9 is (A) 11 √3 square units (B) 12 √3 square units (C) 9 √3 square units (D) 6 √3 square units

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5198ac0c68fe79b7d27531d8eaa9915c-.png" /> Required area =2 ∫0√3(2 x2+9-5 x2) d x =2[9 x - x 3]0√3 =2[9 √3-3 √3]=12 √3

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

$113$ square units

$123$ square units

$93$ square units

$63$ square units

Required area $= 2 \int_{0}^{3} (2 x^{2} + 9 - 5 x^{2}) d x$
$= 2 [9 x - x^{3}]_{0}^{3}$
$= 2 [93 - 33] = 123$

Q. The area of the region : R={(x,y):5x2≤y≤2x2+9} is

113​ square units

123​ square units

93​ square units

63​ square units