Find f'(1) if f(x)=the integral (1+(X^3))^(1/2). Is this a trick question? cause it's asking for the derivative, and the integral is already in derivative form, would i just plug in 1 and get the square root of 2?

Question

anonymous · Answer

this usually is for definite integrals, its the fundamental theorem of the calculus part 1

anonymous · Answer

yeah but it's an indefinite

anonymous · Answer

so is that right to just plug in 1?

anonymous · Answer

http://www.wolframalpha.com/input/?i=derivative+of+integral+%281%2B%28X%5E3%29%29%5E%281%2F2%29

anonymous · Answer

a crazy answer comes up in wolfram, not sure how to get to it tho

zehanz · Answer

These functions are often defined as (e.g.):$$f(x) = \int\limits_{0}^{x}\sqrt{1+p^3}dp$$A variable other than x is used in the integral to avoid misinterpretation: x is the variable of the function f, which is defined by the integral, by evaluating it from 0 to x.

In your case, there is only an indefinite integral given, so it does seem to be a trick question...
To calculate f'(1), you can indeed just plug in 1 in the integrand to get sqrt 2. (IMO)

zarkon · Answer

I wouldn't say it it a trick question...I'd say it is an easy question