The area bounded by the curves y = x - 1 2 , y = x + 1 2 and y = 1 4 is

Step-by-step solution

The curves y = x - 1 2 , y = x + 1 2 and y = 1 4 are shown as where point of intersection are x - 1 2 = 1 4 ⇒ x = 1 2 and x + 1 2 = 1 4 ⇒ x = - 1 2 ∴ Q 1 2 , 1 4 and R - 1 2 , 1 4 ∴ Required area = 2 ∫ 0 1 / 2 x - 1 2 - 1 4 dx = 2 x - 1 3 3 - 1 4 x 0 1 / 2 = 2 - 1 8 · 3 - 1 8 - - 1 3 - 0 = 8 2 4 = 1 3 sq unit