Login

Welcome, Guest. Please login or register.

March 29, 2024, 11:22:08 pm

Author Topic: Antidifferentiation By Deduction  (Read 4207 times)  Share 

0 Members and 1 Guest are viewing this topic.

squance

  • Guest
Antidifferentiation By Deduction
« on: October 30, 2007, 10:38:11 am »
0
Can someone please give me an example of how this works??? What's the likelihood of this being in the exam?

cara.mel

  • Guest
Antidifferentiation By Deduction
« Reply #1 on: October 30, 2007, 10:50:26 am »
0
Do you mean like:
a) Differentiate this
b) Hence, antidifferentiate this?
or something else

reg

  • Guest
Antidifferentiation By Deduction
« Reply #2 on: October 30, 2007, 11:17:33 am »
0
Integration by recognition is what my textbook calls it. IMO it (can be/is) the hardest thing on the course.

Collin Li

  • VCE Tutor
  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4957
  • Respect: +17
Antidifferentiation By Deduction
« Reply #3 on: October 30, 2007, 11:49:55 am »
0
Quote from: "reg"
Integration by recognition is what my textbook calls it. IMO it (can be/is) the hardest thing on the course.


It is probably one of the easiest things to do. There is no thinking required, just follow the steps that VCAA hand out for you. It's also a matter of setting out your notation well:

Example

a. Find the derivative of xlogx with respect to x.
d[xlogx]/dx = (1)*logx + x*(1/x) = logx + 1
(I strongly recommend this notation because it will be clear how to proceed in the next step)

b. Hence, find the antiderivative of logx.
Integrate both sides with respect to x:
=> xlogx = INTEGRATE[logx] + x
=> INTEGRATE[logx] = xlogx - x
(The anti-derivative cancels out with the derivative)

That's what you yield algebraically. You should however, note that there is a constant of integration within that integral. Your general solution would be:

INTEGRATE[logx] = xlogx - x + C

edited to correct for a stupid mistake; thanks Ahmad

Ahmad

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1296
  • *dreamy sigh*
  • Respect: +15
Antidifferentiation By Deduction
« Reply #4 on: October 30, 2007, 11:56:53 am »
0
Check your working carefully!  8)
Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

The collage of ideas. The music of reason. The poetry of thought. The canvas of logic.


asa.hoshi

  • Victorian
  • Forum Obsessive
  • ***
  • Posts: 321
  • Respect: +1
Antidifferentiation By Deduction
« Reply #5 on: October 30, 2007, 12:46:05 pm »
0
prefect exam 1 question i reckon.
I KNOW WHAT YOU DID LAST SUMMER!!

Eriny

  • The lamp of enlightenment
  • Honorary Moderator
  • ATAR Notes Superstar
  • *******
  • Posts: 2954
  • Respect: +100
Antidifferentiation By Deduction
« Reply #6 on: October 30, 2007, 02:46:27 pm »
0
I actually like integration by recognition. I can do it! Besides, they practically give you the answer anyway.

Collin Li

  • VCE Tutor
  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4957
  • Respect: +17
Antidifferentiation By Deduction
« Reply #7 on: October 30, 2007, 05:15:09 pm »
0
Quote from: "Ahmad"
Check your working carefully!  8)


Thanks, I should know by now that whenever you end up with a numerically defined constant from integrating, you've done something wrong, lol.

2happy

  • Victorian
  • Forum Regular
  • **
  • Posts: 84
  • Respect: 0
Antidifferentiation By Deduction
« Reply #8 on: October 30, 2007, 08:19:03 pm »
0
i dont think it''ll be on the exam1
e: 16 year old against them: 17-18 year olds

NO EXAMS left this year

Spesh, Kehm, Fysiks, Ing, C SL 2008


                  _________
Mix it Up TM

melanie.dee

  • Victorian
  • Forum Obsessive
  • ***
  • Posts: 477
  • Respect: +1
Antidifferentiation By Deduction
« Reply #9 on: October 30, 2007, 08:23:58 pm »
0
how come? im thinking it'll definitely be there. and i hate it! along with the entire rest of the methods course. although im strangely attracted to doing a bit of study for methods at the moment.. must be that looming english exam haha. trying to put off study for that 8)

2happy

  • Victorian
  • Forum Regular
  • **
  • Posts: 84
  • Respect: 0
Antidifferentiation By Deduction
« Reply #10 on: October 30, 2007, 08:29:37 pm »
0
theyve got other more important things to test
e: 16 year old against them: 17-18 year olds

NO EXAMS left this year

Spesh, Kehm, Fysiks, Ing, C SL 2008


                  _________
Mix it Up TM

Toothpaste

  • pseudospastic
  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1648
  • Member #10
  • Respect: +26
Antidifferentiation By Deduction
« Reply #11 on: October 30, 2007, 08:52:58 pm »
0
No they don't.

It's a likely question.

2happy

  • Victorian
  • Forum Regular
  • **
  • Posts: 84
  • Respect: 0
Antidifferentiation By Deduction
« Reply #12 on: October 30, 2007, 08:56:54 pm »
0
exam 2 mcq
e: 16 year old against them: 17-18 year olds

NO EXAMS left this year

Spesh, Kehm, Fysiks, Ing, C SL 2008


                  _________
Mix it Up TM

asa.hoshi

  • Victorian
  • Forum Obsessive
  • ***
  • Posts: 321
  • Respect: +1
Antidifferentiation By Deduction
« Reply #13 on: October 30, 2007, 10:35:56 pm »
0
i believe it is a likely question in exam 1. because they didn't test it last year. this question can test student's differential and anti-differential skills/techniques. if its not on exam 1, it will be on exam 2 FOR SURE (i think)!

they're probably fit in a related-rates question in exam 1 as well since it wasn't in last year's paper.
I KNOW WHAT YOU DID LAST SUMMER!!