# Find a curve through the region in the XY-plane whose length from X=0 to X=1 is L=INTEGRATION sqrt 1+1/4e^xdx?

##### 1 Answer

May 27, 2018

#### Explanation:

I'm assuming we have

#int_0^1 sqrt(1 + 1/4e^x)dx#

We can compare to the formula for arc length

#int_a^b sqrt(1 + (dy/dx)^2) dx#

So we have that

We now integrate.

#y = e^(x/2) + C#

Thus an example of the curve would be

Hopefully this helps!