# How do you use the second fundamental theorem of Calculus to find the derivative of given #int cos(sqrt( t))dt# from #[6, x]#?

##### 1 Answer

Mar 15, 2016

#### Answer:

See the explanation below.

#### Explanation:

The second Fundamental Theorem of Calculus (a.k.a The Fundamental Theorem of Calculus, Part 2) tells us that

where

That is, where

Now,

Therefore,

# = d/dx(F(x)) - 0#

# = F'(x) = f(x) = cos(sqrt(x))#

**Note that** I did not find an expression for