How do you use the second fundamental theorem of Calculus to find the derivative of given int tan(t) dt from [1, x]?

Oct 26, 2016

See below

Explanation:

the FTC tells us that

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

We can apply that directly here as:
$\frac{d}{\mathrm{dx}} {\int}_{1}^{x} \tan \left(t\right) \setminus \mathrm{dt} = \tan \left(x\right)$