|
| 21 Dec 2012 01:51 PM |
INT[(e^x)(cos x)dx]
It took a while to figure out, but it's a good problem.
Respect points if you can do it. |
|
|
| Report Abuse |
|
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
|
| 21 Dec 2012 02:01 PM |
doesn't look like integration by parts will work
both e^x and cos x differentiate / integrate infinitely
hmm
i'm thinking |
|
|
| Report Abuse |
|
|
|
| 21 Dec 2012 02:02 PM |
| It helps to write everything out. |
|
|
| Report Abuse |
|
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
|
| 21 Dec 2012 02:29 PM |
maybe parts will work
perhaps the integral is a product of an exponent & a trig functions like
(1/2)e^x cos x + (1/2)e^x cos x
hmm
i think the integral is the sum of two products of e^x and trig functions
like
(1/2)(e^x)(sinx + cosx)
yes that differentiates to give
(1/2)(e^x)(sinx + cosx - sinx + cosx) = (1/2)(e^x)(2cosx) = e^x * cosx
pro |
|
|
| Report Abuse |
|
|
| |
|
brent21
|
  |
| Joined: 20 Oct 2008 |
| Total Posts: 8192 |
|
|
| 21 Dec 2012 02:31 PM |
I don't understand half of this...
Of course, I don't understand Trigonometry either.
;) |
|
|
| Report Abuse |
|
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
|
| 21 Dec 2012 02:36 PM |
"ITT: nerds"
just lol
"I don't understand half of this...
Of course, I don't understand Trigonometry either."
for reference: i am at college level and this exceeds my curricular understanding |
|
|
| Report Abuse |
|
|
|
| 21 Dec 2012 02:37 PM |
Wtf That looks so hard What are you, in college? |
|
|
| Report Abuse |
|
|
|
| 21 Dec 2012 02:38 PM |
This is how I solved it:
INT[(e^x)(cos x)dx] = (e^x)(cos x) + INT[(e^x)(-sin x)dx]
(using integration by parts)
INT[(e^x)(cos x)dx] = (e^x)(cos x) - INT[(e^x)(sin x)dx]
(making it cleaner)
INT[(e^x)(cos x)dx] = (e^x)(cos x) - ((e^x)(sin x) + INT[(e^x)(cos x)dx])
(more integration by parts)
INT[(e^x)(cos x)dx] = (e^x)(cos x) - (e^x)(sin x) - INT[(e^x)(cos x)dx]
(distributing the -1)
2(INT[(e^x)(cos x)dx]) = (e^x)(cos x) - (e^x)(sin x)
(adding "INT[(e^x)(cos x)dx]" to both sides)
INT[(e^x)(cos x)dx] = ((e^x)(cos x) - (e^x)(sin x))/2
(dividing both sides by 2)
INT[(e^x)(cos x)dx] = (e^x)(cos x - sin x)/2
(making it cleaner) |
|
|
| Report Abuse |
|
|
Rushour3
|
  |
| Joined: 13 Jan 2009 |
| Total Posts: 55501 |
|
|
| 21 Dec 2012 02:38 PM |
@whoever mentioned trig
i don't remember this in trig
even though we spent like 2 weeks on it last year |
|
|
| Report Abuse |
|
|
| |
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
|
| 21 Dec 2012 02:41 PM |
@awsome:
k your method was much pro-er than my sheer intuition |
|
|
| Report Abuse |
|
|
|
| 21 Dec 2012 02:43 PM |
It took me so long to realize I could just add that to both sides-
I wasn't thinking of it as an equation. |
|
|
| Report Abuse |
|
|
tumpi2000
|
  |
| Joined: 11 Apr 2012 |
| Total Posts: 2855 |
|
|
| 21 Dec 2012 02:43 PM |
| we OT.Ot=/= meth nerdz r bst |
|
|
| Report Abuse |
|
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
|
| 21 Dec 2012 02:49 PM |
wait, your method gave me the idea for a neater method
letting v = cosx => dv/dx = cosx:
int(e^x cosx) = e^x cosx + int(e^x sinx)
letting v = sinx => dv/dx = cosx:
int(e^x cosx) = e^x sinx - int(e^x sinx)
adding the two equations:
2int(e^x cosx) = e^x sinx + e^x cosx int(e^x cosx) = (1/2)(e^x(sinx + cosx) |
|
|
| Report Abuse |
|
|
| |
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
|
| 21 Dec 2012 02:50 PM |
"letting v = cosx => dv/dx = cosx:"
should be
"letting v = cosx => dv/dx = -sinx:" |
|
|
| Report Abuse |
|
|
|
| 21 Dec 2012 02:50 PM |
| Sorry- I was addressing my own post when I said that.... |
|
|
| Report Abuse |
|
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
| |
|
|
| 21 Dec 2012 02:52 PM |
Umm.... most of us aren't in college yet...
When life gives you Lemons, you get hand squeezed Lemonade. |
|
|
| Report Abuse |
|
|
goof333
|
  |
| Joined: 27 Aug 2008 |
| Total Posts: 16615 |
|
| |
|
|
| 21 Dec 2012 02:56 PM |
| Do you spend your free time looking up math problems? Who would use this in everyday life? |
|
|
| Report Abuse |
|
|
| |
|
jimmy2054
|
  |
| Joined: 10 Jul 2009 |
| Total Posts: 27662 |
|
| |
|
sdfgw
|
  |
 |
| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
|
|
| 21 Dec 2012 03:07 PM |
| i should post more calculus threads just to scare and confuse OT |
|
|
| Report Abuse |
|
|