# Thread: Understanding intergration

1. ## Understanding intergration

the weekend i have a calc test.. the teacher says that we must know if the problem needs intergration by parts without him stating that. i m really not sure how i would know this.. for the most part the book we use divides the homework into sections using substition, intergration by parts, long division, etc..

so i guess my question is.. how do i know when i have to use intergration by part?

also any general advice on mastering intergration (anything u find helpful) will be helpful for me. thanks.

2. Originally Posted by Legendsn3verdie

so i guess my question is.. how do i know when i have to use intergration by part?
It really depends of the problem.

For example, you have an integral, and any sub. you tried didn't work out, then from there think to make an integration by parts. Not always works, it depends of your integration skills and practice.

The key of the integration by parts (or partial integration) is to get a remaining integral on the RHS so that we can easily tackle it, or may be apply partial integration again to see what we can find.

3. Originally Posted by Legendsn3verdie
the weekend i have a calc test.. the teacher says that we must know if the problem needs intergration by parts without him stating that. i m really not sure how i would know this.. for the most part the book we use divides the homework into sections using substition, intergration by parts, long division, etc..

so i guess my question is.. how do i know when i have to use intergration by part?

also any general advice on mastering intergration (anything u find helpful) will be helpful for me. thanks.
another thing to keep in mind. it is generally best to try substitution first. you have to make sure that whatever you substitute, its derivative is somewhere else in the integrand (or can easily be constructed without compicating the problem too much). if that doesn't work, then go on to integration by parts or whatever.

there are certain kinds of integrals that you should know to use by parts on right off the bat. look up problems like these. you should be able to find them in the integration by parts section of your homework. also look up substitution. try to notice patterns. "well, if the integrand looks like this, then chances are i should use substitution, because for a lot of my homework problems that looked like this, i used substitution"

4. Originally Posted by Krizalid
It really depends of the problem.

For example, you have an integral, and any sub. you tried didn't work out, then from there think to make an integration by parts. Not always works, it depends of your integration skills and practice.

The key of the integration by parts (or partial integration) is to get a remaining integral on the RHS so that we can easily tackle it, or may be apply partial integration again to see what we can find.
what do u mean by rhs?? i see u are the intergration master.. when u are doing intergration with limits.. how do u know to either use the uppor or the lower number on the intergral sign as the limit??

5. Originally Posted by Legendsn3verdie
what do u mean by rhs?? i see u are the intergration master.. when u are doing intergration with limits.. how do u know to either use the uppor or the lower number on the intergral sign as the limit??
RHS means right hand side

as for you limit question, i do not understand what you're asking. the fundamental theorem of calculus tells you how to deal with limits. you have to consider both limits, not just one...

6. Originally Posted by Legendsn3verdie
what do u mean by rhs??
"RHS" typically stands for "Right-Hand Side."

Originally Posted by Legendsn3verdie
when u are doing intergration with limits.. how do u know to either use the uppor or the lower number on the intergral sign as the limit??
Are you talking about improper integrals? Could you clarify your question?

7. Originally Posted by Legendsn3verdie
the weekend i have a calc test.. the teacher says that we must know if the problem needs intergration by parts without him stating that. i m really not sure how i would know this.. for the most part the book we use divides the homework into sections using substition, intergration by parts, long division, etc..

so i guess my question is.. how do i know when i have to use intergration by part?
I think its only practice that can help you.

Originally Posted by Legendsn3verdie
also any general advice on mastering intergration (anything u find helpful) will be helpful for me. thanks.
The best way to learn them is by doing them.

Have you ever thought of searching this forum for integration problems?
I think reading Krizalid's posts is one of the better ways to learn integration. Also in mathlinks site, you can read kunny's nice integration questions. Almost all the times, someone or the other answers it elegantly.

8. Originally Posted by Reckoner
"RHS" typically stands for "Right-Hand Side."

Are you talking about improper integrals? Could you clarify your question?

yes improper intergrals is what i m talking about.. usually u need to input ur limit into the problem as u solve.. how do u know if u take the limit of the upper or lower number?

9. Originally Posted by Isomorphism
I think its only practice that can help you.

The best way to learn them is by doing them.

Have you ever thought of searching this forum for integration problems?
I think reading Krizalid's posts is one of the better ways to learn integration. Also in mathlinks site, you can read kunny's nice integration questions. Almost all the times, someone or the other answers it elegantly.
well i m studyin from a calc book right now.. (james stewart) if ur farmiliar.. but i will take al ook around ty.

10. Originally Posted by Legendsn3verdie
well i m studyin from a calc book right now.. (james stewart) if ur farmiliar.. but i will take al ook around ty.
Sorry I have not heard of that book.Is there a free copy available on the net?

11. Originally Posted by Legendsn3verdie
yes improper intergrals is what i m talking about.. usually u need to input ur limit into the problem as u solve.. how do u know if u take the limit of the upper or lower number?
Well that depends. There are several cases:

1. If you have $\int_a^\infty f(x)\,dx$, evaluate $\lim_{b\to\infty}\int_a^bf(x)\,dx$.

2. If you have $\int_{-\infty}^bf(x)\,dx$, evaluate $\lim_{a\to-\infty}\int_a^bf(x)\,dx$.

3. If you have $\int_{-\infty}^\infty f(x)\,dx$, split it up into $\int_{-\infty}^cf(x)\,dx + \int_c^\infty f(x)\,dx$, for some constant $c$.

4. If you have $\int_a^b f(x)\,dx$, where f has an infinite discontinuity at a point $c$ on $(a, b)$, then split up the integral and evaluate as follows:

$\int_a^b f(x)\,dx\Rightarrow\int_a^c f(x)\,dx + \int_c^b f(x)\,dx$

$\Rightarrow\lim_{b\to c-}\int_a^b f(x)\,dx + \lim_{a\to c+}\int_a^b f(x)\,dx$

12. Ooh-oohh i have that book!

13. Hello,

I'll just point out a thing... If you want to understand integration, you should understand its writing : integration, and not inteRgration

Plus, how can you recognize when you have to do a substitution ? Try to find the main function and see if its derivative appears.

$\int f'(x)f^n(x) \ dx=\frac{f^{n+1}(x)}{n+1}$

$\int \frac{f'(x)}{f(x)} \ dx=\ln(|f(x)|)$

$\int \frac{f'(x)}{1+f^2(x)} \ dx=\arctan \left(f(x)\right)$

~~~~~~~~~~~~~~
$\int \sqrt{1-x^2} dx$ --> substitute for $t=\cos(x)$ or $t=\sin(x)$

$\int \sqrt{1+x^2} dx$ --> substitute for $t=\sinh(x)$

$\int \sqrt{x^2-1} dx$ --> substitute for $t=\cosh(x)$

This is certainly not exhaustive.