1 Attachment(s)

area under curve and line.

The diagram shows a sketch of part of the curve with equation *y*=*x*2+1 and the line with equation *y*=7−*x*. The finite region *R*1 is bounded by the line and the curve. The finite region *R*2 is below the curve and the line and is bounded by the positive *x*- and *y*-axes as shown in the diagram.

(a) Find the area of *R*1.

(b) Find the area of *R*2.

$\displaystyle 7-x = x^2 + 1 $

$\displaystyle 0 = x^2 + x -6 $

$\displaystyle 0 = (x+3) (x-2) $

$\displaystyle x = 2 , x = -3 $

Area of R1 = $\displaystyle \int_{-3}^2 [ 7-x-x^2 + 1] dx $

I can work this out, but How would I go about working the area of region 2? Becasue there's also the area of region 1 inside region 2.