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

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