Calc

Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus.

intergral s^2/(1+3s^4) ds from sqrtx to 1

F'(x)=?

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  1. Find the most general antiderivative of f(x)=–8e^x–6secant^2(x), where -pi/2<x<pi/2

    Note: Any arbitrary constants used must be an upper-case "C"

    F(x)=?

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  2. ∫[√x,1] s^2/(1+3s^4) ds

    Are you sure there's no typo here? As you can see here

    http://www.wolframalpha.com/input/?i=%E2%88%ABs^2%2F%281%2B3s^4%29+ds

    this is not an integral I'd expect to find. If you meant

    ∫[√x,1] s^3/(1+3s^4) ds

    then it's a lot easier:

    1/12 log(1+3s^4) [√x,1]
    = 1/12 (log(1+3x^2)-log(4))
    = 1/12 log((1+3x^2)/4)

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