Section 5.3.  Read the entire section.  Pay particular attention to the fundamental theorem of calculus (FTC) on page 393.  Answer the following questions.  Send an e-mail with subject line MA251 to selliott@utm.edu .

1) Finish the sentence:  [Newton and Leibniz] saw that the Fundamental Theorem enabled them to compute . . . .

1) To compute areas easily without having to compute them as limits of sums

Mason Cullen


2) Use the fundamental theorem of calculus part 1 (and maybe Example 2) to answer this question:  What is

d/dx [Integral from 0 to x] t^3 dt  ?

x^3
Deonte Johnson


3) Finish this sentence about FTC part 2.  It's very surprising that [a definite integral], which was defined by a complicated procedure involving all of the values of f(x) for [an interval], can be found by . . . .

knowing the values of F(x) at only two points, a and b.

Denton Davolt