Integration

sleepyescapade

Hi Im looking for notes on Integration, cant seem to find any online that I can understand easily. If anyone has any suggestions i'd love to hear from you. Thankyou

Cokehead Mother

megcork wrote: »

Hi Im looking for notes on Integration, cant seem to find any online that I can understand easily. If anyone has any suggestions i'd love to hear from you. Thankyou

What can't you understand in particular?

sleepyescapade

The method of substitution and integration by parts

Cost Boy!!

less stress more success revision books go through integration very well.

Challenged

These might help.

http://studentxpress.ie/papers/integration.htm

http://studentxpress.ie/educ/maths/maths3/maths3.html

The Walsho

Thanks for those links guys, integration is such a bastard.

conzy

I will integrate you!

sleepyescapade

Thank you so much, i will check those out

irish_boy90

i found the book had everything i needed.
try looking up the chapter and it on your old copy.
Go through the method.

Same thing everytime. (esp with by parts, all you need to know in the formula, thats in the loggbook and the word LIATE (Late with an i, helps me remember it))

iodine

[Obviously this doesn't have the proper maths symbols but I will use £ as the integral sign]

£udv = uv - £vdu

Basically for integration by parts you have an equation you want to integrate over that has "two parts"

eg £ (sin x)(x)dx

And what you want to do is separate out the two bits before you can integrate properly, since there is no product rule for integration like in differentiation.

So by separating them I mean letting one bit = u and the other = dv The LIATE rule mentioned above is an easy way to work out how to separate them. It stands for

Logs
Inverse Trig
Algebra
Trig
Exponential

Basically you look at the two parts in your equation and see which one appears first on your list and let that one = u. So with my example I have an algebra part (x) and a trig function (sin x). Since algebra is higher on the list it gets the u and the rest of the equation ie the sinx dx is then equal to dv.

Once you have worked out which bit goes with what you'll have two equations, one with "u =" and one with "dv= "

so in my example you have

u = x
dv = sinx dx (It is very important that you remember the dx aswell otherwise the next part doesn't make sense)

So take the u and differentiate it with respect to x, so now you have
du/dx =

And take the "dv =" and integrate both sides to get
v =

So I have du/dx = 2
and you can bring the dx to the otherside so you have;
du = 2dx

and £dv = £sinx dx
v = cos x

Now use the formula given at the begining.

£udv = uv - £vdu

= (x)cos x - £(cos x)2dx
= x cos x -2£(cos x)dx (you can take the 2 outside the integral because
it is a constant)
= x cos x - 2(- sin x)
= x cos x +2(sin x)

So this is your answer. It's been a couple of years since I did the leaving so I'm not sure what they teach about the limits on the integral but that is the basic method for it.

I hope this helped, I'm not sure how clear my explanation is and you'll probably get a better run through in the less stress books or even your school books.

sleepyescapade

Thank you very much

MathsManiac

And by the way, here's a cool joke about integration that someone else posted to the maths jokes thread in the maths forum:

An exponential walks into a bar. He pulls up a bar stool sits down and asks the barman for a pint.

Over in the corner there's a large group of functions: sines, cosines, logs, all sitting around having a laugh telling jokes and sharing stories.

The barman comes over and asks the exponential why he's all alone and not over having fun with the other functions.

The exponential answers in a low voice, "I tried to integrate but nothing happened".

The Walsho

MathsManiac wrote: »

And by the way, here's a cool joke about integration that someone else posted to the maths jokes thread in the maths forum:

An exponential walks into a bar. He pulls up a bar stool sits down and asks the barman for a pint.

Over in the corner there's a large group of functions: sines, cosines, logs, all sitting around having a laugh telling jokes and sharing stories.

The barman comes over and asks the exponential why he's all alone and not over having fun with the other functions.

The exponential answers in a low voice, "I tried to integrate but nothing happened".

I'm giving that to my maths teacher in the morning!

~Candy~

right!! i love Integration

ok , my adive is

just do the different types of questions over and over again..

simple ones ..
let u= ,
logs
cos
sin
sin^-1
cos^-1
e^x
...

even power of sin, cos, odd power of sin and cos, odd and even powers of sin and cos , sinA+sinB ...

PG 9 of the log table is really impoart there..

jaycummins

heres a physics joke:

a neutron goes into a bar and asks for a beer from the bartender. The bartender brings him the beer and the neutron asks "How much is that?"

The bartender replies "For you sir, no charge."
_______

Two oxygen atoms are walking down the street. One says "Hey i think i just lost an electron!!"
The other says "are you sure"
He replies "Ye, I'M POSITIVE!"

since we're on the subject of jokes