The area of the region bounded by the curves x²+y²=8 and y²=2 x is

Step-by-step solution

Given curves, aligned x²+y² &=8...(i) and y² &=2 x...(ii) aligned On solving Eqs. (i) and (ii), we get aligned x²+2 x-8 &=0 x²+4 x-2 x-8 &=0 x(x+4)-2(x+4) &=0 (x-2)(x+4) &=0 x=2 and y &= 2 aligned Required area array l =2[ Area of O A P+ Area of P A B] =2 [ ₀² 2 x d x+ ₂^ 2 2 8-x² d x ] =2 [ 2 (x^ 3 / 2 2 3 )₀²+ ( x 2 8-x² . . . .+ 8 2 ⁻¹ x 2 2 )₂^ 2 2 ] =2 [ 2 2 3 (2^ 3 / 2 )+4 2 -2-4 4 ] array =2 [ 2 2 3 2 2 +2 -2- ]=2 [ 8 3 -2+ ]=2 ( 2 3 + )=2 + 4 3