(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The statement says:using the calculus fundamental theorem find:

[tex]\displaystyle\frac{d}{dx}(\displaystyle\int_{2}^{x}\displaystyle\frac{t^{3/2}}{\sqrt[ ]{t^2+17}}dt)[/tex]

3. The attempt at a solution

I thought that what I should do is just to apply Barrow, and then I'd have:

[tex]\displaystyle\frac{d}{dx}(\displaystyle\int_{2}^{x}\displaystyle\frac{t^{3/2}}{\sqrt[ ]{t^2+17}}dt)=-\displaystyle\frac{x^{3/2}}{\sqrt[ ]{x^2+17}}[/tex]

Is this right?

I've tried it on the hard way too, but then:

[tex]t=\sqrt[ ]{17}\sinh u[/tex]

[tex]dt=\sqrt[ ]{17}\cosh u du[/tex]

[tex]\displaystyle\frac{d}{dx}(\displaystyle\int_{2}^{x}\displaystyle\frac{t^{3/2}}{\sqrt[ ]{t^2+17}dt})=\displaystyle\frac{d}{dx}(\sqrt[3]{17}\displaystyle\int_{2}^{x}\sqrt[3]{\sinh^2 u}du)[/tex]

I don't know how to solve the last integration.

Bye there.

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# Homework Help: Derivative and integral using calculus foundamental theorem

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