Fundamental Theorem of Calculus to find the derivative of the function

**tom@ballooncalculus** · November 20th 2009, 09:00 AM

Firstly,

$G(x) = \int_x^6 \cos(\sqrt{2t}) dt = - \int_6^x \cos(\sqrt{2t}) dt$

The FTC says it then follows that $G'(x) = -\cos(\sqrt{2x})$

Just in case a picture helps...

... and in this case...

... where straight continuous lines differentiate downwards (integrate up) with respect to x.

Spoiler:

__________________________________________

Don't integrate - balloontegrate!

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