derivative of an integral?

**yoman360** · October 8th 2009, 04:29 PM

$\int_{\sqrt{x}}^ x \frac{cos z}{z} dz$

I have no idea what to do.

**pickslides** · October 8th 2009, 04:36 PM

You could try integration by parts in the form

$\int_{\sqrt{x}}^ x z^{-1}\cos( z) ~dz$

or use a series approximation for $\cos(z)$

**skeeter** · October 8th 2009, 04:37 PM

Originally Posted by yoman360

$\int_{\sqrt{x}}^ x \frac{cos z}{z} dz$

I have no idea what to do.

the Fundamental Theorem of Calculus ...

$u$ and $v$ are both functions of $x$

$\frac{d}{dx} \left[ \int_v^u f(z) \, dz \right] = f(u) \cdot \frac{du}{dx} - f(v) \cdot \frac{dv}{dx}$

**yoman360** · October 8th 2009, 04:56 PM

Originally Posted by skeeter

the Fundamental Theorem of Calculus ...

$u$ and $v$ are both functions of $x$

$\frac{d}{dx} \left[ \int_v^u f(z) \, dz \right] = f(u) \cdot \frac{du}{dx} - f(v) \cdot \frac{dv}{dx}$

I never seen a problem like this before and now thanks to you i know how to solve it when i see it again

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