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Anyone super awesome at taking anti-derivatives of funtions?

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kepler.
Posts: 8761 - Karma: 139

So I'm in need of someone's help. Just when I thought I was done with my AP Calculus exam my teacher decides to give the same questions we took on it and make us re-do them. Well did that all except for one problem and its driving me crazy. All year I tried to aviod the number e but it came back. So if anyone can help me solve this quick problem I'd be much obliged.

The rate at which tickets were sold for is modeled by r(t) = 550te^-(t/2) tickets per hour. Based on the model, how many tickets were sold by 3 pm (t = 3) to the nearest whole number?

^thats what I have to solve. I've already figured out all I need to do is take the anti derivative to get the funtion and insert 3 for t. The problem is I can't take the antiderivative. Please help. Its the last part of my last problem. I've just spent a good hour and a half on the whole packet and I can't quit now.

And if it helps (I know my notation isn't very clear) but the function should be able to be written as 1/(550te^(t/2)) That negative sign might throw you off. Thanks again

May 12 2008 7:26PM
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user098123
Posts: 6072 - Karma: 18
its just integral of e^(ax) = (1/a)e^(ax)
May 12 2008 7:33PM
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user098123
Posts: 6072 - Karma: 18
for that you will also have to use integration by parts, which isn't too bad.

I'm just going to do it in my head but I think you will get like...

(550t)(e^(-t/2)) - integral:(550)(e^(-t/2))

sooo

500te^(-t/2) + 1100e^(-t/2) and plug in 3 and 0 or something like that.
May 12 2008 7:36PM
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kepler.
Posts: 8761 - Karma: 139
Thanks for the help. Are you sure that the integral of the funtion you put is correct. wouldn't that be the integral if the funtion was 550te^2t rather than 550te^(-t/2)
May 12 2008 7:50PM
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user098123
Posts: 6072 - Karma: 18
no because you take 1/a, so that means it is -1/(1/2) which is just -2, so you multiply by -2 for the integral, and you are initially subtracting the integral, so when you multiply -2 you get plus 110te^(-t/2) or whatever.
May 12 2008 7:53PM
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low_fidelity
Posts: 2673 - Karma: 118
i think the integral function of the hyperbole is(93^8)+92-%(76) and the diameter of the superflous loofa would take the ^3 to be multiplexed by another 85th of the origional hyperbole and subtract the 43^78*(plo9) from the {a5(73[loofa^3]87^9th}7b} .

ya that should help
May 12 2008 7:53PM
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marsland
Posts: 3150 - Karma: 421
that problem sucked so much.  i skipped like half of it.  anyways i did it on my calculator because i couldnt remember if it was noncalc and got 973.  if it is noncalc then im sorry but i dont plan on doing calculus til college
May 12 2008 7:54PM
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user098123
Posts: 6072 - Karma: 18
its really not that bad at all, just need to know the difference between derivatives and integrals of e functions
May 12 2008 7:57PM
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kepler.
Posts: 8761 - Karma: 139
Thanks for the help. I really appreciate it.
May 12 2008 8:03PM
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attitashfreestyle29
Posts: 3070 - Karma: 209
haha i remember that question from the ap exam. The easiest way to do it is to just plug it into your calculator cuz that was in the calculator section of the frqs. Just plug fNint(The Function, x, 0,3) and it'll do it for you. THe fNint button is the 9th thing down under math on a ti-83
May 12 2008 8:03PM
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BootySpunk.
Posts: 8148 - Karma: 84
Damn I can't wait till calc! my brain hurts just reading this shit

and I thought trig was hard
May 12 2008 8:04PM
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kepler.
Posts: 8761 - Karma: 139
Haha thanks. We have to present our solutions in front of class tomorrow and I happened to draw one of the only questions I couldn't do (that is after looking at it after the test) but I'll check your answer with mine once I finish the problem. Thanks everyone again
May 12 2008 8:05PM
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skierdudeguy
Posts: 6574 - Karma: 81
hah.
you think thats bullshit?
my calc teacher is giving two more tests this week. i have no idea why. we just took the fucking AP test!
May 12 2008 8:06PM
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kepler.
Posts: 8761 - Karma: 139
Haha I know the feeling. I thought we we're done with class after AP testing. Apparently not. He says we're learning new stuff next week.
May 12 2008 8:25PM
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marsland
Posts: 3150 - Karma: 421
damnnnnn i would hate to have your teachers.  mine gave us 1 problem that we have til may 28th to do, and he said that about half of us wont be able to do it.  oh, and he got the problems online and we found the site.  sucks that your still having tests and learning shit, but at least youll be well prepared for your next math class
May 16 2008 5:27PM
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ryan.c
Posts: 6592 - Karma: 14
ahhh im doing this now too. i felt so smart that i could help a fellow ns'er out with complicated school work, but its already done
May 16 2008 7:15PM
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kepler.
Posts: 8761 - Karma: 139
Nah I thought the last few weeks of school were going to be bad but I was wrong. My calc/physics teacher was just messing with us when he said we wouldnt stop working till the end of the year.

I have like 6 days of school left and I'm done in all of my classes except AP lit (even though we're reading Macbeth I just sit and read freeskiers all period)

In fact my calc/physics teacher didn't even come to school today. We didn't have a substitute in class all day and I'm in there for 3 periods a day.
May 16 2008 8:25PM
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vinnyT
Posts: 349 - Karma: 10
our calc class got some sweet tee shirts made
they say "I used u for (integral e^x), I knew it was wrong, but it felt so right"
(if you don't get it, the integral sign makes it spell sex, and you wouldn't use u substitution for that expression)
I know, we're nerds
May 16 2008 11:30PM
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marsland
Posts: 3150 - Karma: 421
haha i chuckled a bit.  took me a second to get it but yeah, thats a good one
May 17 2008 1:27AM
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Pisces
Posts: 905 - Karma: 13
haha damn, i remember that question but i havent even thought about calc at all since i took the ap exam. we watched some movie called stand and deliver which was pretty good and about the ap test, and now were slowly learning integration by parts sucks that you have to go over the problems and such.
May 17 2008 11:33AM
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killa_cam
Posts: 13143 - Karma: 15
use integration by parts ∫udv = uv - ∫vdu

when you are deciding which function to be u, it goes, logarithmic, inverse trigonometric, algebraic (polynomial), trigonometric, exponential.

this function is a product of a algebraic and an exponential function, but algebraic is before exponential in that list so you pick t to be u, and dv is e^(-t/2) dt

at the end

∫r(t) dt = -1100 e^(-t/2) (t + 2) + C
May 17 2008 11:36AM
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St.Steezy
Posts: 4228 - Karma: 20
just wait till it become 3 dimension.. oh yeah, multi variable calc is the shit...

Woot for second year math
May 17 2008 8:22PM
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Pawelko
Posts: 203 - Karma: 10
go to
http://calc101.com/
it shows you step by step how to do just about any problem
May 17 2008 8:33PM
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Pawelko
Posts: 203 - Karma: 10
oh, if it asks for a password boat works
May 17 2008 8:34PM
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ThaLetterM.
Posts: 8609 - Karma: 1,612
holy shit i have no idea whats going on
May 17 2008 8:50PM
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cobra_commander
Posts: 16909 - Karma: 4,681
calc is fun, it honestly makes like alot easier.

And I would stop trying to avoid e, it is kinda important.
May 18 2008 1:41AM
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mysterymanjgj
Posts: 411 - Karma: 13
all we do in calc now is play kickball against the other ap classes...
May 18 2008 2:58AM
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