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### Section 5.6 : Definition of the Definite Integral

10. Differentiate the following integral with respect to $$x$$.

$\int_{4}^{x}{{9{{\cos }^2}\left( {{t^2} - 6t + 1} \right)\,dt}}$ Show Solution

This is nothing more than a quick application of the Fundamental Theorem of Calculus, Part I.

The derivative is,

$\frac{d}{{dx}}\left[ {\int_{4}^{x}{{9{{\cos }^2}\left( {{t^2} - 6t + 1} \right)\,dt}}} \right] = \require{bbox} \bbox[2pt,border:1px solid black]{{9{{\cos }^2}\left( {{x^2} - 6x + 1} \right)}}$