Amaths integration ):

iamapebble SG

Hello, anyone who is online now can help me? ^^ You see, let's say I have a question:

Integrate from 3 to 4 for 1/(x-2)^3 dx.

It will be:
Integrate 3 to 4 for (x-2)^-3 dx
= [(x-2)^-2 / -2] 3 to 4
= solve etc.

But I don't understand, by adding 1 to the power and dividing the expression by the new power, we are only integrating the entire expression on itself right? Why don't we have to divide the bolded part by (x^2/2 - 2x) which is obtained from integrating (x-2) itself? In differentiation, I thought we have to differentiate the whole thing on itself and then the separate elements inside too? =[ This is the part I'm super confused on integration, because sometimes I don't divide it and I get it wrong and sometimes I divide it I also get it wrong.

I hope you guys get what I'm trying to say. T.T I've tried to make it as clear as possible already. Thanks sooo much!

skythewood SG

differentiate your answer.

if you get the question back, it works.

integrate is just opposite of differentiate, don't think too deep.

maurizio13 SG

where ish 老鹰？？？

iamapebble SG

But then why is it when I integrate (2+3x)^5 the solutions are:

{ [(2+3x)^6]/6 } / 3

Divided by 3.. I assume it's from 3x? >.< I don't know.. =[

skythewood SG

it is from 3x.

differentiate the answer, you will need to multiply by 3 because of 3x too right?

maurizio13 SG

iamapebble SG

it is from 3x.

differentiate the answer, you will need to multiply by 3 because of 3x too right?

So means, everytime if I divide I'll divide what I integrated with the coefficient of x and not the whole expression over again? Just like integrating 1/(x-2)^3 whereby I actually divide by 1, but because it'll be the same so there is no difference to the answer?

integrate 1/x result is always ln |x|

Yes, that's another question. When do I make it In =[ Alamak, I feel so dumb. -.-"

skythewood SG

Yes, that's another question. When do I make it In =[ Alamak, I feel so dumb. -.-"

yes, you get the idea.

There is no real integrating... there is only a opposite of differentiating..

iamapebble SG

Hmmmm okayyy, thanks I'll go try more questions I guess.. =/

maurizio13 SG

i am very rusty, but i think it's because if the power is -1, there are no anti-derivatives.

skythewood SG

x^-1

integrate will get lnx

this is no technique in this integration, just memorize it.

eagle SG

x^-1

integrate will get lnx

this is no technique in this integration, just memorize it.

There is, but it is out of O level syllabus.

eagle SG

yes, you get the idea.

There is no real integrating... there is only a opposite of differentiating..

the concept of integration is different from differentiation... not fully opposite...
integration is sort of a type of summation, differentiation is a little of finding small differences

then again, out of O level sylalbus :D

secretliker SG

O Level just memorise integrate x^-1 = ln x

Actually when do we need the mod?

ie integrate x^-1 = ln |x|

eagle SG

O Level just memorise integrate x^-1 = ln x

Actually when do we need the mod?

ie integrate x^-1 = ln |x|

everytime need... better to put on the safe side

Garrick_3658 SG

My school never say MUST put leh...

I only learned "integrate 1/x = ln x". That's all. The mod is used to ensure that x > 0 right, since ln x where x < 0 is undefined.

eagle SG

The mod is used to ensure that x > 0 right, since ln x where x < 0 is undefined.

Yup

I was taught in sec sch to put...

Anyway, put won't go wrong. Don't put might go wrong... So I think, put better :D

iamapebble SG

I have no idea what's with the mod and no mod. -catch no ball- o.o

eagle SG

because you cannot ln a negative number

iamapebble SG

OHHHHHH I SEE I SEE! THANKS :D