Question

Find the area of the region bounded by the graphs of the given equations.

Answer 1

Given

`y=x^2+12x+1,y=1-x^2`

Answer

On finding the common points between

`\begin{gathered} y=x^2+12x+1,y=1-x^2 \\ \text{ The graphs intersect at x=0 and x=-6} \\ \text{ Area enclosed = }\int ^0_(-6)|x^2+12x+1-(1-x^2)|dx \\ =72 \end{gathered}`