`y = e^x, y = 2 - x^2` Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find...

`y=e^x, y=2-x^2`

Refer the attached image. Graph of e^x is plotted in red color and graph of y=2-x^2 is plotted in blue color.

From the graph, the x-coordinates of the intersection of the curves are x `~~` -1.3 ,  x `~~` 0.55.

Area of the region bounded by the curves A=`int_(-1.3)^(0.55)((2-x^2)-e^x)dx`

`A=[2x-x^3/3-e^x]_(-1.3)^(0.55)`

`A=[2(0.55)-0.55^3/3-e^0.55]-[2(-1.3)-(-1.3)^3/3-e^(-1.3)]`

`A=(1.1-0.55458333-1.733253018)-(-2.6+0.732333333-0.272531793)`

`A=(-0.688711351)-(-2.14019846)`

`A=-0.688711351+2.14019846`

`A~~1.451487109`

`y=e^x, y=2-x^2`

Refer the attached image. Graph of e^x is plotted in red color and graph of y=2-x^2 is plotted in blue color.

From the graph, the x-coordinates of the intersection of the curves are x `~~` -1.3 ,  x `~~` 0.55.

Area of the region bounded by the curves A=`int_(-1.3)^(0.55)((2-x^2)-e^x)dx`

`A=[2x-x^3/3-e^x]_(-1.3)^(0.55)`

`A=[2(0.55)-0.55^3/3-e^0.55]-[2(-1.3)-(-1.3)^3/3-e^(-1.3)]`

`A=(1.1-0.55458333-1.733253018)-(-2.6+0.732333333-0.272531793)`

`A=(-0.688711351)-(-2.14019846)`

`A=-0.688711351+2.14019846`

`A~~1.451487109`