integration (1 Viewer)

[dawso]

gday all, anyone reckon they can solve this one for me (with commentry please)

int (0 - SQRT(pi/2) x^3 . cos (x^2) dx

in words in case u cant get that is:

(integral from zero to square root of pi on 2 of: x cubed, cos x squared dx)

cheers guys

-dawso

 

[FinalFantasy]

gday all, anyone reckon they can solve this one for me (with commentry please)

int (0 - SQRT(pi/2) x^3 . cos (x^2) dx

in words in case u cant get that is:

(integral from zero to square root of pi on 2 of: x cubed, cos x squared dx)

cheers guys

-dawso

I=int. x³cos(x²) dx from 0 to sqrt(pi\2)
let u=x² and dv\dx=xcos(x²)
du=2x dx and v=int. xcos(x²) dx=1\2 sin(x²)
I=[1\2 sin(x²) x²] from 0 to sqrt(pi\2) -int. xsin(x²) dx
consider int. xsin(x²) dx
let u=x²
du\dx=2x
int. xsin(x²) dx=1\2int. sin u du
den juz put it in and it's done

 

[who_loves_maths]

you're really good at integration aren't you FinalFantasy? i've seen you post clever solutions to almost all integration questions in this forum.

anyways;

Orignally Posted by FinalFantasy
let u=x² and dv\dx=xcos(x²)
du=2x dx and v=int. xcos(x²) dx=1\2 sin(x²)
I=[1\2 sin(x²) x²] from 0 to sqrt(pi\2) -int. xsin(x²) dx
consider int. xsin(x²) dx
let u=x²
du\dx=2x
...

just for those who aren't as experienced as you are at integration and who are probably wondering how/why one would immediately think of approaching this question in the way you did with such ease (esp. just coming up with the first step like you did (in bold)), the more "mundane" first step could also be to use substitution first:
let x^2 = u, so then reduce the original integral to: (1/2)INT[uCos(u)du]
and from this one would probably think of using integration by parts as a more obvious step to take next from here.

 

[~ ReNcH ~]

Over the course of the year you should expose yourself to as many examples as possible. That's really the only way to master topics like Integration and Volumes, just as FinalFantasy has done

 

[haboozin]

the answer is 1 - Pi/2 right?

why does everyone here always do things so weirdly...
i just did subsititution then parts...

 

[FinalFantasy]

you're really good at integration aren't you FinalFantasy? i've seen you post clever solutions to almost all integration questions in this forum.

thanks man, im not dat good but i like integration the most out of the 4unit topics i guess..
but i am so angry about the half yearly now dat we mention it...
in the half yearlies... i was being a complete IDIOT and i spent LOTS of time on the GRAPHS question, and after that.. my mind was all gone, i started rushing the rest of the exam and at the end i ran out of time to do the Integration question(which was where most marks were as well, and it was my best topic)
and i ended up failing dat exam with all those errors from rushing and not answering half the integration part.........
GRRR!

 

[who_loves_maths]

Originally Posted by FinalFantasy
in the half yearlies... i was being a complete IDIOT and i spent LOTS of time on the GRAPHS question, and after that.. my mind was all gone, i started rushing the rest of the exam and at the end i ran out of time to do the Integration question(which was where most marks were as well, and it was my best topic)
and i ended up failing dat exam with all those errors from rushing and not answering half the integration part.........
GRRR!

aww...what a pity. it sucks how your teachers made integration questions appear towards the end of the paper... usually they're at the start (unless they're very hard). but i guess that's why we get reading time to decide how we're going to approach the test...lol, someone from my grade always starts the last question first in every yr12 exam so far (and he hasn't done that badly).
dw about it FinalF, the important thing is to learn from your mistakes i guess. (i often run out of time in exams too, hehe...and i still haven't learnt my lesson yet!)

 

[Antwan23q]

arrgh, teachers are gay at writing tests. i had a term 3 test for 4 unit today. i studied for about a week doing really hard integration. u know the ones where they dont give you the substituions and are really complex, and then it turns out, it was the easiest test ive ever done. i got 100% and finished 20 minutes to go. u would think they would make it the least bit difficult for something like the hsc year.

 

[FinalFantasy]

arrgh, teachers are gay at writing tests. i had a term 3 test for 4 unit today. i studied for about a week doing really hard integration. u know the ones where they dont give you the substituions and are really complex, and then it turns out, it was the easiest test ive ever done. i got 100% and finished 20 minutes to go. u would think they would make it the least bit difficult for something like the hsc year.

hey our teacher is sort of like dat too!
usually he just sets book work questions and everyone can do dem....

 

[who_loves_maths]

hey our teacher is sort of like dat too!
usually he just sets book work questions and everyone can do dem....

that's worst case scenario! the point of school assessments is to spread the candidature out using hard tests so that ppl's ranks matter more and give a better indication of ability against the rest of the cohort.
i hate it when teachers make easy tests, cause most ppl in the grade get 99% or more. everyone's crammed at the top and you don't get to know how good you really are.

 

[FinalFantasy]

that's worst case scenario! the point of school assessments is to spread the candidature out using hard tests so that ppl's ranks matter more and give a better indication of ability against the rest of the cohort.
i hate it when teachers make easy tests, cause most ppl in the grade get 99% or more. everyone's crammed at the top and you don't get to know how good you really are.

but at the end.. the trials will sort things out(we have to do CSSA trials which is supposedly hard)

 

[Antwan23q]

actualy i got 100%, everyone else barely passed...

 

[FinalFantasy]

actualy i got 100%, everyone else barely passed...

ooer, so atleast ur efforts weren't futile....
i studied for the half yearly test a lot, and it was a book work test and bcoz of wat happend i failed it LoL now i am like 10% worth of assessment marks behind 3-4 ppl
dunno if i can still get a 90 now..

 

[~ ReNcH ~]

hey our teacher is sort of like dat too!
usually he just sets book work questions and everyone can do dem....

Except for our Conics exam....that was a decent exam. I consider myself fairly lucky to get 71% but by the same token I should've been able to get around 80%.

 

[~ ReNcH ~]

ooer, so atleast ur efforts weren't futile....
i studied for the half yearly test a lot, and it was a book work test and bcoz of wat happend i failed it LoL now i am like 10% worth of assessment marks behind 3-4 ppl
dunno if i can still get a 90 now..

Even though easy tests don't spread out the candidature, it's important that you don't lose marks for silly things. You can't rely on a difficult test to stuff everyone else up and make you stand out. You must also ensure that if you get an easy test that you get 100% or close to it.

 

[FinalFantasy]

Even though easy tests don't spread out the candidature, it's important that you don't lose marks for silly things. You can't rely on a difficult test to stuff everyone else up and make you stand out. You must also ensure that if you get an easy test that you get 100% or close to it.

yea, dat i didn't manage to do, and im most pissed about half yearly which i could've done so much better

 

[~ ReNcH ~]

yea, dat i didn't manage to do, and im most pissed about half yearly which i could've done so much better

Well, exam technique is also important. If you think about it, there was no real difference between doing Graphs in the first 30 mins and then doing the rest (as you did) and doing Graphs in the last 30 mins as I did. Ultimately, it just gives you a psychological boost as opposed to giving you a physical advantage.

 

[FinalFantasy]

Well, exam technique is also important. If you think about it, there was no real difference between doing Graphs in the first 30 mins and then doing the rest (as you did) and doing Graphs in the last 30 mins as I did. Ultimately, it just gives you a psychological boost as opposed to giving you a physical advantage.

yea i realised exam techniques are crucial...
well i was just mad on that day.. was gone crazy lol
*slaps myself on the head*

 

[~ ReNcH ~]

yea i realised exam techniques are crucial...
well i was just mad on that day.. was gone crazy lol
*slaps myself on the head*

Ah well, focus on the trials and pull me up in the HSC exam

 

[FinalFantasy]

Ah well, focus on the trials and pull me up in the HSC exam

lol YOU better get 97+ or else ur gonna cause some bad effects on us damn u!!