Free Area between two curves challenge Practice Problems • Learn To Be

Define two functions by

f(x)=e^x

and

g(x)=x^3+2x^2

.

The graphs of

f

and

g

enclose the shaded region shown below:

Which one of these expressions represents the area of the region?

Choose 1 answer:

A
$\displaystyle \int_{-1.96}^{+0.93}\left(x^3+2x^2-e^x\right)dx$
B
$\displaystyle \int_{-1.96}^{-0.62}\left(e^x-x^3-2x^2\right)dx ~+ \int_{-0.62}^{+0.93}\left(x^3+2x^2-e^x\right)dx$
C
$\displaystyle \int_{-1.96}^{-0.62}\left(x^3+2x^2-e^x\right)dx ~+ \int_{-0.62}^{+0.93}\left(e^x-x^3-2x^2\right)dx$
D
$\displaystyle \int_{-1.96}^{+0.93}\left(e^x-x^3-2x^2\right)dx$

Area between two curves challenge