* Site-Outage Notice: Our engineering elves will be tweaking the Shmoop site from Monday, December 22 10:00 PM PST to Tuesday, December 23 5:00 AM PST. The site will be unavailable during this time.
© 2014 Shmoop University, Inc. All rights reserved.
The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

Example 1

Suppose JoJo was driving 30 mph at 5 pm and 40 mph at 7 pm. How far did she travel between 5 and 7 pm?

Example 2

The velocity of a racing snail, in feet per second, is given below.

How far does the racing snail travel

(a) from t = 0 to t = 10 seconds?

(b) from t = 10 to t = 15 seconds?

(c) from t = 15 to t = 25 seconds?

(d) from t = 0 to t = 25 seconds?

Example 3

A bug moves along a numberline with velocity v(t) in units per second given by the graph below.

If the bug is at 3 on the numberline when t = 0 seconds, where is the bug when

(a) t = 3 seconds?

(b) t = 5 seconds?

Noodle's College Search