Let Δ be the area of the region x , y ∈ ℝ 2 : x 2 + y 2 ≤ 21 , y 2 ≤ 4 x , x ≥ 1 . Then 1 2 Δ - 21 sin - 1 2 7 is equal to

Step-by-step solution

Plotting the diagram of x 2 + y 2 ≤ 21   &   y 2 ≤ 4 x for x ≥ 1 we get, Now from above diagram required Area Δ = 2 ∫ 1 3 2 x d x + 2 ∫ 3 21 21 - x 2 d x ⇒ Δ = 8 3 3 3 - 1 + 21 sin - 1 2 7 - 6 3 So, 1 2 Δ - 21 sin - 1 2 7 = 1 2 8 3 3 3 - 1 + 21 sin - 1 2 7 - 6 3 - 21 sin - 1 2 7 = 1 2 8 3 3 3 - 1 - 6 3 = 2 3 - 8 3 2 = 3 - 4 3