The area (in sq. units) of the region x , y ∈ R 2 4 x 2 ≤ y ≤ 8 x + 12 is

Question

The area (in sq. units) of the region x , y &#8712; R 2 4 x 2 &#8804; y &#8804; 8 x + 12 is

Aicharya · Accepted Answer

4 x 2 = y y = 8 x + 12 4 x 2 = 8 x + 12 x 2 - 2 x - 3 = 0 x = - 1 , 3 A = &#8747; - 1 3 8 x + 12 - 4 x 2 d x A = 8 x 2 2 + 12 x - 4 x 3 3 3 - 1 = 4 9 + 36 - 36 - 4 - 12 + 4 3 = 36 + 8 - 4 3 = 44 - 4 3 = 132 - 4 3 = 128 3

The area (in sq. units) of the region x , y &#8712; R 2 4 x 2 &#8804; y &#8804; 8 x + 12 is

Solution

The area (in sq. units) of the region x , y ∈ R 2 4 x 2 ≤ y ≤ 8 x + 12 is