hey, guys and gals,
just wanted to see if any of you can direct me towards the correct way of
approaching this problem.
the problem asks to find the arc length of y=e^2x
now ive obtained the derivative dy/dx to be
2e^2x and when I use the formula for finding the
arclength, I then have the integral:
∫√(1+(2e^2x )²) dx
next I use
u=√(1+(2e^2x )²)
so that if I square both sides I get:
u²=1+4e^4x then, to get du:
2udu=16e^4x dx
now i noticed that above in "u²=1+4e^4x " i could solve for
e^4x to =(u²-1)/4 so that in the equation,
2udu=16e^4x dx, i could also solve for e^4x dx=1/8udu, then substituting
the e^4x=(u²-1)/4 into e^4x dx=1/8udu to become
(u²-1)/4 dx=1/8udu then solving for dx, I found
dx=u/2(u²-1) du
so my question is what do you do next? I substituted back u and du
into the integral and get u²/2(u²-1) du but I dont know where to go from here. Can somebody please help?
thanks in advance for your efforts,
07 Yamaha R6