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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

3. 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.

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# Using integrals to calculate arc length

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