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Re: I saw this wonderful math problem today:

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awsomeness7878 is not online. awsomeness7878
Joined: 23 Nov 2008
Total Posts: 9512
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.
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sdfgw is not online. sdfgw
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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
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awsomeness7878 is not online. awsomeness7878
Joined: 23 Nov 2008
Total Posts: 9512
21 Dec 2012 02:02 PM
It helps to write everything out.
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sdfgw is not online. sdfgw
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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
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JohnEntwistle is not online. JohnEntwistle
Joined: 04 May 2012
Total Posts: 4195
21 Dec 2012 02:30 PM
[ Content Deleted ]
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brent21 is not online. 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.

;)
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sdfgw is not online. sdfgw
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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
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imbored332 is not online. imbored332
Joined: 27 Feb 2011
Total Posts: 15284
21 Dec 2012 02:37 PM
Wtf
That looks so hard
What are you, in college?
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awsomeness7878 is not online. awsomeness7878
Joined: 23 Nov 2008
Total Posts: 9512
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)
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Rushour3 is not online. 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
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JohnEntwistle is not online. JohnEntwistle
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21 Dec 2012 02:38 PM
[ Content Deleted ]
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sdfgw is not online. sdfgw
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21 Dec 2012 02:41 PM
@awsome:

k your method was much pro-er than my sheer intuition
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awsomeness7878 is not online. awsomeness7878
Joined: 23 Nov 2008
Total Posts: 9512
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.
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tumpi2000 is not online. tumpi2000
Joined: 11 Apr 2012
Total Posts: 2855
21 Dec 2012 02:43 PM
we OT.Ot=/= meth nerdz r bst
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sdfgw is not online. sdfgw
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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)
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awsomeness7878 is not online. awsomeness7878
Joined: 23 Nov 2008
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21 Dec 2012 02:49 PM
+ C

so much for pro....
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sdfgw is not online. sdfgw
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21 Dec 2012 02:50 PM
"letting v = cosx => dv/dx = cosx:"

should be

"letting v = cosx => dv/dx = -sinx:"
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awsomeness7878 is not online. awsomeness7878
Joined: 23 Nov 2008
Total Posts: 9512
21 Dec 2012 02:50 PM
Sorry- I was addressing my own post when I said that....
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sdfgw is not online. sdfgw
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21 Dec 2012 02:50 PM
"+ C"

ffffffff
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Pritchard264 is not online. Pritchard264
Joined: 11 Nov 2012
Total Posts: 520
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.
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goof333 is not online. goof333
Joined: 27 Aug 2008
Total Posts: 16615
21 Dec 2012 02:54 PM
GAH! E_E
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scoobysnacks1 is not online. scoobysnacks1
Joined: 20 Nov 2010
Total Posts: 9590
21 Dec 2012 02:56 PM
Do you spend your free time looking up math problems? Who would use this in everyday life?
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christhebrick is not online. christhebrick
Joined: 23 Feb 2017
Total Posts: 13045
21 Dec 2012 02:58 PM
ow my brain
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jimmy2054 is not online. jimmy2054
Joined: 10 Jul 2009
Total Posts: 27662
21 Dec 2012 03:00 PM
My eyes are in pain.
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sdfgw is not online. sdfgw
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21 Dec 2012 03:07 PM
i should post more calculus threads just to scare and confuse OT
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