The area bounded by the curve y^2=2 x+1 and the straight line x-y-1=0 is given by

Step-by-step solution

The point of intersection of curve y^2=2 x+1 and line x-y-1=0 is (14,3) and (0,-1) Required area = _ -1 ^3 (x₂-x₁ ) d y aligned & = _ -1 ^3 (y+1)- (y^2-1 ) 2 d y & = 1 2 _ -1 ^3 (2 y+3-y^2 ) d y & = 1 2 [y^2+3 y- y^3 3 ]_ -1 ^3 & = 1 2 [(9+9-9)- (1-3+ 1 3 ) ] & = 1 2 (9+ 5 3 ) & = 16 3 sq units aligned