Consider a region R = x ,   y ∈ R 2 : x 2 ≤ y ≤ 2 x . If a line y = α divides the area of region R into two equal parts, then which of the following is true ?

Question

Consider a region R = x , &#160; y &#8712; R 2 : x 2 &#8804; y &#8804; 2 x . If a line y = &#945; divides the area of region R into two equal parts, then which of the following is true ?

Aicharya · Accepted Answer

&#8747; 0 4 y - y 2 d y = 2 &#8747; 0 &#945; y - y 2 d y 2 y 3 / 2 3 - y 2 2 0 4 = 2 2 y 3 / 2 3 - y 2 4 0 &#945; &#8658; 16 3 - 4 = 2 2 3 &#945; 3 / 2 - &#945; 2 4 &#8658; &#160;&#160; 4 3 = 2 2 3 &#945; 3 / 2 - &#945; 2 4 &#8658; &#160;&#160; 2 3 = 8 &#945; 3 / 2 - 3 &#945; 2 12 &#8658; &#160;&#160; 8 &#945; 3 / 2 - 3 &#945; 2 = 8 &#8658; 3 &#945; 2 - 8 &#945; 3 / 2 + 8 = 0

Consider a region R = x ,   y ∈ R 2 : x 2 ≤ y ≤ 2 x . If a line y = α divides…

Solution

Consider a region R = x , &#160; y &#8712; R 2 : x 2 &#8804; y &#8804; 2 x . If a line y = &#945; divides…

Solution

Consider a region R = x , y ∈ R 2 : x 2 ≤ y ≤ 2 x . If a line y = α divides…