If the line x = α divides the area of the region R = { x , y ∈ R 2 : x 3 ≤ y ≤ x ,   0 ≤ x ≤ 1 } into two equal parts, then

Question

If the line x = &#945; divides the area of the region R = { x , y &#8712; R 2 : x 3 &#8804; y &#8804; x , &#160; 0 &#8804; x &#8804; 1 } into two equal parts, then

Aicharya · Accepted Answer

A = ∫ 0 1 x - x 3 d x = 1 4 Area of curvilinear triangle O P Q = A 2 = 1 8 ⇒ ∫ 0 1 x - x 3 d x = 1 8 ⇒ 2 α 4 - 4 α 2 + 1 = 0 ⇒ α 2 - 1 2 = 1 2 ⇒ α 2 = 2 - 1 2 so α lies between 0.5 and 1

If the line x = α divides the area of the region R = { x , y ∈ R 2 : x 3 ≤ y ≤ x ,…

Solution

If the line x = &#945; divides the area of the region R = { x , y &#8712; R 2 : x 3 &#8804; y &#8804; x ,…

Solution

If the line x = α divides the area of the region R = { x , y ∈ R 2 : x 3 ≤ y ≤ x ,…