Study Guides
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1.
Antiderivatives Help
Introduction to Antiderivatives Many processes, both in mathematics and in nature, involve addition. You are familiar with the discrete process of addition, in which you add finitely many numbers to obtain a sum or aggregate. But there are ...
Source: McGraw-Hill Professional -
2.
Area Under a Curve Help
Introduction to Area Under a Curve Consider the curve shown in Fig. 4.1. The curve is the graph of y = f ( x ). We set for ourselves the task of calculating the area A that is (i) under the curve, (ii) above ...
Source: McGraw-Hill Professional -
3.
Signed Area Help
Introduction to Signed Area Without saying so explicitly, we have implicitly assumed in our discussion of area in the last section that our function f is positive, that is its graph lies about the x-axis. But of course many functions do not share ...
Source: McGraw-Hill Professional -
4.
The Area Between Two Curves Help
Introduction to The Area Between Two Curves Frequently it is useful to find the area between two curves. See Fig. 4.17. Following the model that we have set up earlier, we first note that the intersected region has left endpoint at x = a ...
Source: McGraw-Hill Professional -
5.
Rules of Integration Help
Rules of Integration We have been using various rules of integration without enunciating them explicitly. It is well to have them recorded for future reference. Linear Properties
Source: McGraw-Hill Professional -
Source: McGraw-Hill Professional
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7.
The Indefinite Integral Help
Introduction to The Indefinite Integral In practice, it is useful to have a compact notation for the antiderivative. What we do, instead of saying that “the antiderivative of f (x) is F(x) + C ,” is to ...
Source: McGraw-Hill Professional -
8.
The Fundamental Theorem of Calculus Help
Introduction to The Fundamental Theorem of Calculus The most important idea in all of calculus is that it is possible to calculate an integral without calculating Riemann sums and passing to the limit. This is the Fundamental Theorem of Calculus, due to Leibniz ...
Source: McGraw-Hill Professional -
9.
Areas Under Curves Study Guide
Areas Under Curves Around the same time that so many great mathematicians devoted themselves to figuring out the slopes of tangent lines, other mathematicians were working on an entirely different problem. They wanted to be able to figure out the area underneath ...
Source: LearningExpress, LLC -
10.
The Fundamental Theorem of Calculus Study Guide
The Fundamental Theorem of Calculus Here comes the resounding climax of calculus. It would be best to read this lesson with some bombastic orchestral music like that of Wagner or Orff. This, however, is not necessary. The initial question here is innocent enough: ...
Source: LearningExpress, LLC
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