# Thread: Fundamental Theorem of Calculus to find the derivative of the function

1. ## Fundamental Theorem of Calculus to find the derivative of the function

2. Firstly,

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

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

Just in case a picture helps...

... and in this case...

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

Spoiler:

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Don't integrate - balloontegrate!

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Balloon Calculus Drawing with LaTeX and Asymptote!