Report, edit, etc...Posted by BeeR_KeG on 2006-03-09 at 20:33:27
Alright, so I had a Calculus test yesterday and since the class was 45 minutes, none of us could finish a test desinged for 2 hours, so the teacher gave us the rest of the part today. When I turned in my exam yesterday, everybody was asking me how to do the second to last problem. I always do my exams in order, so I never reached that problem. I told them to go figure it out themselves because then I'd attempt on doing it and just memorize the proccess, which I hate doing. So today everybody says that it's impossible to do and plan to boycott the problem. So we take the exam and I skipped the second to last problem just for dibs. I started my timer when I was goign to start that problem, 2:37 minutes to do the problem, what took most of my friends over 8 hours to attempt, and could never finish, took me 2 and a half minutes.
I don't know if it's that I'm incredibly smart or I'm in a Calculus class that isn't very competent. I'm going to give you guys the problem to see for myself. Please display the process.
[sub]π/4[/sub]
∫[Sin³2xCos2x]dx
[sup]π/8[/sup]
I don't know if it's that I'm incredibly smart or I'm in a Calculus class that isn't very competent. I'm going to give you guys the problem to see for myself. Please display the process.
[sub]π/4[/sub]
∫[Sin³2xCos2x]dx
[sup]π/8[/sup]
Report, edit, etc...Posted by Urmom(U) on 2006-03-09 at 20:51:46
Hmm you must be smart, I'm in Geometry so I wouldn't know how to do it but that is why you should go to MIT. 
gogogo massachussetts
gogogo massachussetts
Report, edit, etc...Posted by Syphon on 2006-03-09 at 20:52:29
Well you are icredibly smart. And I know the feeling of being surrounded by incompetence.
Report, edit, etc...Posted by CheeZe on 2006-03-09 at 22:14:14
Assuming π = pi or something.
I'm going to guess this (I'm 100% sure I'm wrong
):
1/4-1/(sqrt(2)*4)
<-- doesn't show work because he wasn't paying attention in class over integration.
I'm going to guess this (I'm 100% sure I'm wrong
):1/4-1/(sqrt(2)*4)
<-- doesn't show work because he wasn't paying attention in class over integration.
Report, edit, etc...Posted by DT_Battlekruser on 2006-03-09 at 23:07:54
Oh wait, thanks cheeze, I thought what is Pi in Tahoma was an n, and I was like wtf? That's ridiculously easy.
∫[sub]π/8,π/4[/sub] sin[sup]3[/sup](2x)cos(2x) dx
[(1/8)sin[sup]4[/sup](2x)│[sub]π/8,π/4[/sub]
(1/8)[sin(π/2)][sup]4[/sup] - (1/8)[sin(π/4)][sup]4[/sup]
(1/8)(1)[sup]4[/sup] - (1/8)(√(2)/2)[sup]4[/sup]
(1/8) - (1/8)(4/16)
(1/8) - (1/32)
(4/32) - (1/32)
(3/32)
Right?
Took me 6 minutes, but I did it all on the screen and without a calculator. I vote your calc class is stupid. I'm terrible at fractional arithmetic so I might have screwed up integrating by hand.
Woops, 1/8 = 4/32, not 8/32. Told ya. It's correct now; checked on my TI-84+ Silver Edition.
∫[sub]π/8,π/4[/sub] sin[sup]3[/sup](2x)cos(2x) dx
[(1/8)sin[sup]4[/sup](2x)│[sub]π/8,π/4[/sub]
(1/8)[sin(π/2)][sup]4[/sup] - (1/8)[sin(π/4)][sup]4[/sup]
(1/8)(1)[sup]4[/sup] - (1/8)(√(2)/2)[sup]4[/sup]
(1/8) - (1/8)(4/16)
(1/8) - (1/32)
(4/32) - (1/32)
(3/32)
Right?
Took me 6 minutes, but I did it all on the screen and without a calculator. I vote your calc class is stupid. I'm terrible at fractional arithmetic so I might have screwed up integrating by hand.
Woops, 1/8 = 4/32, not 8/32. Told ya. It's correct now; checked on my TI-84+ Silver Edition.
Report, edit, etc...Posted by Shapechanger on 2006-03-09 at 23:11:29
Holy shiz, I feel stupid.
Report, edit, etc...Posted by CheeZe on 2006-03-09 at 23:31:01
Ah DTBK. I knew it was either 1/4 or 1/8. Didn't bother to check. 
Oh well, I was half right.
(I forgot to multiply the 1/4 by 1/2... I feel stupid)
Oh well, I was half right.
(I forgot to multiply the 1/4 by 1/2... I feel stupid
)Report, edit, etc...Posted by DT_Battlekruser on 2006-03-09 at 23:33:32
Yeah, the 2 in the 2x chains out too cheeze
Report, edit, etc...Posted by Shapechanger on 2006-03-09 at 23:35:39
YOU feel stupid? I was lost up to the point he started to simplify the fractions...Something tells me Honors Calculus wont be fun next year....
Report, edit, etc...Posted by CheeZe on 2006-03-09 at 23:39:49
And the fact that I forgot to make it to the power of 4.
Here's a slightly more difficult problem:
∫x^2/(x^2+1)
Here's a slightly more difficult problem:
∫x^2/(x^2+1)
Report, edit, etc...Posted by 5(U) on 2006-03-10 at 12:01:16
QUOTE(DT_Battlekruser @ Mar 9 2006, 11:07 PM)
Oh wait, thanks cheeze, I thought what is Pi in Tahoma was an n, and I was like wtf? That's ridiculously easy.
∫[sub]π/8,π/4[/sub] sin[sup]3[/sup](2x)cos(2x) dx
[(1/8)sin[sup]4[/sup](2x)│[sub]π/8,π/4[/sub]
(1/8)[sin(π/2)][sup]4[/sup] - (1/8)[sin(π/4)][sup]4[/sup]
(1/8)(1)[sup]4[/sup] - (1/8)(√(2)/2)[sup]4[/sup]
(1/8) - (1/8)(4/16)
(1/8) - (1/32)
(4/32) - (1/32)
(3/32)
Right?
Took me 6 minutes, but I did it all on the screen and without a calculator. I vote your calc class is stupid. I'm terrible at fractional arithmetic so I might have screwed up integrating by hand.
Woops, 1/8 = 4/32, not 8/32. Told ya. It's correct now; checked on my TI-84+ Silver Edition.
[right][snapback]442446[/snapback][/right]
∫[sub]π/8,π/4[/sub] sin[sup]3[/sup](2x)cos(2x) dx
[(1/8)sin[sup]4[/sup](2x)│[sub]π/8,π/4[/sub]
(1/8)[sin(π/2)][sup]4[/sup] - (1/8)[sin(π/4)][sup]4[/sup]
(1/8)(1)[sup]4[/sup] - (1/8)(√(2)/2)[sup]4[/sup]
(1/8) - (1/8)(4/16)
(1/8) - (1/32)
(4/32) - (1/32)
(3/32)
Right?
Took me 6 minutes, but I did it all on the screen and without a calculator. I vote your calc class is stupid. I'm terrible at fractional arithmetic so I might have screwed up integrating by hand.
Woops, 1/8 = 4/32, not 8/32. Told ya. It's correct now; checked on my TI-84+ Silver Edition.
[right][snapback]442446[/snapback][/right]
i did it with my TI-83 + which isnt silver edition and we got the same answer..
my conclusion is: u paid more to get the TI-84 silver edition and its useless ;-)
ADDITION:
QUOTE(CheeZe @ Mar 9 2006, 11:39 PM)
And the fact that I forgot to make it to the power of 4.
Here's a slightly more difficult problem:
∫x^2/(x^2+1)
[right][snapback]442481[/snapback][/right]
Here's a slightly more difficult problem:
∫x^2/(x^2+1)
[right][snapback]442481[/snapback][/right]
cool ill try it but i dont have much time left..
Report, edit, etc...Posted by Centreri on 2006-03-10 at 14:43:30
I need to learn what the pretty sign at the beginning of the problem is called & what it does..
And the big E would be nice too.
And the big E would be nice too
.Report, edit, etc...Posted by DT_Battlekruser on 2006-03-10 at 19:16:49
QUOTE
i did it with my TI-83 + which isnt silver edition and we got the same answer..
my conclusion is: u paid more to get the TI-84 silver edition and its useless ;-)
Doubt it. I found my TI-84+ Silver on the ground at school
.Report, edit, etc...Posted by Mune'R0x on 2006-03-10 at 23:13:15
Who needs math anyways? Not me. Especially when I got good ole cocai... Uhhh... Nevermind.
Report, edit, etc...Posted by T-MaStAA on 2006-03-10 at 23:38:14
you forgot to carry the 1 
.
.Report, edit, etc...Posted by BeeR_KeG on 2006-03-11 at 10:38:48
QUOTE(DT_Battlekruser @ Mar 10 2006, 12:07 AM)
∫[sub]π/8,π/4[/sub] sin[sup]3[/sup](2x)cos(2x) dx
[(1/8)sin[sup]4[/sup](2x)│[sub]π/8,π/4[/sub]
(1/8)[sin(π/2)][sup]4[/sup] - (1/8)[sin(π/4)][sup]4[/sup]
(1/8)(1)[sup]4[/sup] - (1/8)(√(2)/2)[sup]4[/sup]
(1/8) - (1/8)(4/16)
(1/8) - (1/32)
(4/32) - (1/32)
(3/32)
[right][snapback]442446[/snapback][/right]
Yes, the answer is correct, I did it this way:
π/4
∫[Sin³2xCos2x]dx
π/8
π/4
∫[Sin²2xSin2xCos2x]dx
π/8
Let:
u=Sen²2x
du=4Sin2xCos2xdx
du/4Sin2xCos2x=dx
u[sub]1[/sub]=Sin²(π/2)
u[sub]1[/sub]=1
u[sub]2[/sub]=Sin²(π/2)
u[sub]2[/sub]=1/2
1
∫[uSin2xCos2x]du/4Sen2xCos2x
1/2
1
∫[u/4]du
1/2
u²/8 ][sup]1[/sup][sub]1/2[/sub]
(1)²/8 - (1/2)²/8
1/8 - (1/8)(1/4)
1/8 - 1/32
3/32
Report, edit, etc...Posted by A_of_s_t on 2006-03-11 at 13:35:28
Holy!!! Im going to be in H. Calc. and crap! Im going to die! I have calc for dummies, would that help?
Report, edit, etc...Posted by Urmom(U) on 2006-03-11 at 14:35:56
QUOTE
∫[uSin2xCos2x]du/4Sen2xCos2x
lol, SEN is taking over Calculus.
Report, edit, etc...Posted by BeeR_KeG on 2006-03-12 at 11:05:37
Sen is how we write Sin in spanish.
Sine = Seno
Sin = Sen
Sine = Seno
Sin = Sen