The area of the region bounded by the curves, y²=8 x and y=x is

Step-by-step solution

Given curves, y²=8x...(i) and y=x...(ii) On solving Eqs. (i) and (ii), we get aligned x²-8 x &=0 x(x-8) &=0 x &=0,8 aligned and y=0,8 aligned Required area, (O P A) &= ₀⁸( 8 x -x) d x &= [2 2 2 3 x^ 3 / 2 - x² 2 ]₀⁸ aligned = 4 2 3 (8)^ 3 / 2 - (8)² 2 = 4 2 3 (2)³ 2 2 - 64 2 = 16 3 8- 64 2 =64 ( 2 3 - 1 2 )=64 (4-3) 6 =64 1 6 = 32 3