# Calculus Integral Excersices

• alba_ei
But even if you only do a couple problems from each book, you'll still be better off than most students.

#### alba_ei

Wich is the best book to obtain excercises of integrlas for practice for an exam? I mean should i concentrate on 1 book or is vbest try various?
Another question: which is the book where are the most difficult integrals? if you know various please write them from the one that contain the easier to the harder excersices

just look for a table of integrals and try to prove each of them...if you can manage this then you should be fine on a test

try this one on for size

$$\int{\frac{x}{e^{x}-1}}dx$$

between 0 and infinity

How do you do that? I tried with int. by parts, a sub won't work that I can see. I did it on the integrals.wolfram.com and it had a Li function.

you use the fact that the integral goes from 0 to infinity.

I believe that the integral can be solved by dividing the top and bottom by $$e^{-x}$$ expand it as a geometric series, and integrate term by term from 0 to infinity.

Alba, do you happen to have a calculus book by James Stewart? If not, you can probably get one at your school's library (it might be a special version like "early transcendentals," or "early vectors," it doesn't really matter). Depending on what version you've got, either chapter 7 or chapter 8 will be on techniques of integration. The first four sections are on integration by parts, trigonometric products, inverse trigonometric substitution, and partial fractions. You can work a couple problems from each section to practice specific techniques.

The fifth section of this chapter contains about fifty integrals (I might be off on that number). The catch here is that they don't tell you what technique to use. You need to figure that out on your own. If your exam is on integration, then just work as many problems as you can comfortably do before the test, and you should be very well prepared. Remember that the key with mathematics is to practice as many problems as you can. As my dad always says, you need to have "extreme familiarity with the material."

Anyway, I hope that helps!

Last edited:
arunma said:
Alba, do you happen to have a calculus book by James Stewart? If not, you can probably get one at your school's library (it might be a special version like "early transcendentals," or "early vectors," it doesn't really matter). Depending on what version you've got, either chapter 7 or chapter 8 will be on techniques of integration. The first four sections are on integration by parts, trigonometric products, inverse trigonometric substitution, and partial fractions. You can work a couple problems from each section to practice specific techniques.

The fifth section of this chapter contains about fifty integrals (I might be off on that number). The catch here is that they don't tell you what technique to use. You need to figure that out on your own. If your exam is on integration, then just work as many problems as you can comfortably do before the test, and you should be very well prepared. Remember that the key with mathematics is to practice as many problems as you can. As my dad always says, you need to have "extreme familiarity with the material."

Anyway, I hope that helps!

i see the book of stewart and have a lot of excersices i was watching other books like spiavak but is a little strange so i think that the stewart's book its going to be helpful thanks for the reference

tim_lou said:
you use the fact that the integral goes from 0 to infinity.

I believe that the integral can be solved by dividing the top and bottom by $$e^{-x}$$ expand it as a geometric series, and integrate term by term from 0 to infinity.

Bingo! That is exactly the way to do it.

alba_ei said:
i see the book of stewart and have a lot of excersices i was watching other books like spiavak but is a little strange so i think that the stewart's book its going to be helpful thanks for the reference

I'm glad you're finding it helpful. To be honest, I'd say that you don't need to bother looking at multiple books. After all, fifty integrals is a lot of problems. And there are only so many permutations of the same problem that you can be given (after all, even the most creative textbook author can only write up so many variations of inverse trigonometric substitution). If somehow you manage to do every problem in that section, and get all the answers right, then I'd be surprised if you don't ace an exam on integration.

## What is a calculus integral exercise?

A calculus integral exercise is a mathematical problem that involves finding the area under a curve using calculus techniques. It typically involves solving an integral, which is a mathematical representation of the area under a curve.

## What is the purpose of practicing calculus integral exercises?

Practicing calculus integral exercises helps to develop problem-solving skills and strengthens understanding of calculus concepts. It also prepares students for more complex applications of calculus, such as in physics and engineering.

## How do I solve a calculus integral exercise?

To solve a calculus integral exercise, you must first identify the function and limits of integration. Then, you can use various integration techniques, such as substitution or integration by parts, to find the antiderivative. Finally, evaluate the antiderivative at the limits of integration to find the area under the curve.

## What are some common mistakes to avoid when solving calculus integral exercises?

Some common mistakes to avoid when solving calculus integral exercises include forgetting to include the constant of integration, making algebraic errors when integrating, and not properly identifying the limits of integration. It is important to carefully follow the steps and check your work for accuracy.

## Are there any resources available to help me practice calculus integral exercises?

Yes, there are many resources available to help you practice calculus integral exercises. These include textbooks, online tutorials, practice problems, and study groups. It is also helpful to seek assistance from a teacher or tutor if you are struggling with a particular concept.