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?
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!