How to find The points of intersection of y = x2 + 1 and y = x + 1 in this question Share with your friends Share 0 Ankita Agarwal answered this Dear Student , The required region is the intersection of the following regions A1={(x,y):0≤y≤x2+1} It represents the region below the parabola y=x2+1 A2={(x,y):0≤y≤x+1}. It represents the region below the straight line y = x + 1, and A3={(x,y):0≤x≤2}. It represents the region lying between the ordinates x=0 and x=2. The required area is the region shown as the shaded region in the following figure By solving y=x+1 and y=x2+1, we get the points of intersection A(0, 1) and B (1, 2). Hence the required region is bounded by y=f(x),y=0,x=0,x=2, Where f(x)=x2+1,0≤x≤1x+1,1≤x≤2 ∴ Required area A=∫02f(x)dx=∫01x2+1dx+∫12x+1dx =x33+x01+x22+x12=13+1+42+2-12-1=43+52=236 Regards 0 View Full Answer
