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# Calculus: The Integral Help & Practice Problems

Find study help on the integral for calculus. Use the links below to select the specific area of the integral you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn the integral for calculus.

### Study Guides

showing 1 - 10 of 14
• 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 ...

• 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 ...

• 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 ...

• 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 ...

• 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

• 6.

#### The Integral Practice Test

Review the following concepts if needed: Antiderivatives Help

• 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 ...

• 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 ...

• 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 ...

• 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: ...

• 1

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