# How do you use the Fundamental Theorem of Calculus to find the derivative of int sqrt (2 + sec 7t) from x to pi?

Jul 24, 2016

$= - \sqrt{2 + \sec 7 x}$

#### Explanation:

$\frac{d}{\mathrm{dx}} {\int}_{x}^{\pi} \sqrt{2 + \sec 7 t} \setminus \mathrm{dt} q \quad \star$

by FTC part 2, $\frac{d}{\mathrm{dx}} {\int}_{a}^{x} \setminus f \left(t\right) \setminus \mathrm{dt} = f \left(x\right)$

so $\star$ becomes

$- \frac{d}{\mathrm{dx}} {\int}_{\pi}^{x} \sqrt{2 + \sec 7 t} \setminus \mathrm{dt}$

$= - \sqrt{2 + \sec 7 x}$