Just started Calc II last month, it's been smooth so far but I've run into a bit of snag involving the application of integrals in the calculation of arc length.
The formula you use is the definite integral of (1+(d/dx)^2)^.5.
Often once you derive the d/dx and square it, you're left with a somewhat nasty looking equation under the radical. Deriving this square root is what's giving me the trouble. Is there any particular technique?
Here's one example:
Y= ((x^4)/8) + 1/4x^2, In the interval [1,2]
Y'= (x^3)/2 - 1/2x
The Attempt at a Solution
(1+(x^(3/2) - 1/2x)^2)^.5
I need to integrate this from 1 to 2, but how does can one easily transform ut into an integrable form using algebra!
EDIT: I should mention that the textbook indicated that integrals involving arc lentgh are "often very difficult to evaluate" yet proceeded to present examples where such integration was smoothly carried out.