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

Define two functions by

f(x)=\dfrac{x}{\sqrt{x^2+1}}

and

g(x)=(x-1)^2

.

Let

S

be the region enclosed by the graphs of

f

and

g

:

Which of these integrals represents the area of region $S$ ?

Choose all answers that apply:

A
$\displaystyle \int_{1.94}^{0.39}\left(\dfrac{x}{\sqrt{x^2+1}}-(x-1)^2\right)dx$
B
$\displaystyle \int_{0.39}^{1.94}\left((x-1)^2-\dfrac{x}{\sqrt{x^2+1}}\right)dx$
C
$\displaystyle \int_{0.39}^{1.94}\left(\dfrac{x}{\sqrt{x^2+1}}-(x-1)^2\right)dx$
D
$\displaystyle \int_{1.94}^{0.39}\left((x-1)^2-\dfrac{x}{\sqrt{x^2+1}}\right)dx$

Area between two curves challenge