2.4 The Fundamental Theorem of Calculus Part II
In the previous section we discussed the first part of The Fundamental Theorem of
Calculus. It said that we can evaluate a definite integral by first evaluating the
corresponding indefinite integral F(x) = .
2.2 Definite Integrals
Definite integrals calculate areas of regions in the plane. For example, the definite
integral of y = x2 from x = 1 to x = 3 is the area of the region R that is bounded by the
parabola y = x2, the x-axis and the lines x = 1 and x =
2. Integrals
As we mentioned earlier, calculus revolves around two main concepts, derivatives and
integrals.
1.
Derivatives:
We have seen that derivatives correspond physically to an
instaneous rate of change of one variable y which is related to
another
2.3 The Fundamental Theorem of Calculus Part I
We have talked about two types of integrals, namely indefinite integrals (also called
antiderivatives) and definite integrals.
The indefinite integral of a function y = f(x) is simply a function whose derivat
1.6 Examples of Derivatives Arising in Different Subjects
1.6.1 Marginal Costs
A company produces windshield wiper blades for cars. Let
x = the number of blades they will produce this week
C = C(x) = cost (in dollars) of producing the x blades
Perhaps the
1. Derivatives
Calculus revolves around two main concepts, derivatives and integrals.
1.
Derivatives:
Physically a derivative corresponds to a rate of change. If your
car's speedometer reads 20 miles per hour, then this is the value of
a certain derivativ
Math 115
Exam 1
Fall 2011
Name: _ This is a closed book exam. You may use a calculator and the
formulas handed out with the exam. You may find that your calculator can do some of the
problems. If this is so, you still need to show how to do the problem by
Final Exam Part 1
Math 115
Fall 2011
Name: _ For this first question you may use the formulas handed out with the
exam and a non-graphing calculator, but NOT a graphing calculator. Show all work and explain any
reasoning which is not clear from the comput
Exam #4
Math 115
Winter 2012
Name: _ This is a closed book exam. You may
use a calculator and the formulas handed out with the exam. Show all work and explain any
reasoning which is not clear from the computations. (This is particularly important if I am
Math 115
Exam 3 Part 1
Fall 2011
Name:_ This is a closed book exam. For this first question you
may use the formulas handed out with the exam and a non-graphing calculator, but NOT a
graphing calculator. Show all work and explain any reasoning which is no
Math 115
Exam 3 Part 1
Winter 2012
Name:_ This is a closed book exam. For this first question you
may use the formulas handed out with the exam and a non-graphing calculator, but NOT a
graphing calculator. Show all work and explain any reasoning which is