I'm kinda new to this forum, but I'm currently in AB Calc and I understand it very well, so if anyone has any questions about calc or w/e, I'd be glad to try and help. Just let me know! :)
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here's a tricky one just for fun. Take the integral of sinxcosx using substitution.
Substituting u:=sinx then du = cosxdx and you get the integral of udu = (sin^2x)/2
Substituting u:=cosx then du = -sinxdx and you get the integral of -udu = -(cos^2x)/2
(sin^2x)/2 = -(cos^2x)/2
(1-cos^2x)/2 = -(cos^2x)/2
1/2 - (cos^2x)/2 = -(cos^2x)/2
1/2 = 0
1 = 0
Cool huh.
You know you're an AP student if...
you think studying is fun.
you constantly find yourself saying "we had homework?"
everything you know about sex, you learned in english class.
If you try to fail, and succeed, which have you done?
AHA, not true. What you have is:
udu = -udu
here's how it should go...
(sin^2x)/2 = (cos^2x)/2
(1-cos^2x)/2 = (cos^2x)/2
1-cos^2x = cos^2x
1 = 2cos^2x
1/2 = cos^2x
cos^-1(1/2) = 2x
2x = pi/4 , 7pi/4
x = pi/8 , 7pi/8
[=RoyalBlue][=Comic Sans MS]
"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," say Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It
you do realize that we were solving an INDEFINITE integral. Are you saying that indefinite integrals only work when x = pi/8 or 7pi/8?
You know you're an AP student if...
you think studying is fun.
you constantly find yourself saying "we had homework?"
everything you know about sex, you learned in english class.
If you try to fail, and succeed, which have you done?
I'm not suggesting anything of the sort. I never integrated, and neither did you.:p If you did integrate you'd get something like....
Well, I'd tell you if I had paper and a pencil :p
[=RoyalBlue][=Comic Sans MS]
"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," say Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It
umm, I definitely integrated it during my first post. I used u substitution, for one of them I used u:=sinx and for the other I used u:=cosx. I have no clue what you are trying to do...
You know you're an AP student if...
you think studying is fun.
you constantly find yourself saying "we had homework?"
everything you know about sex, you learned in english class.
If you try to fail, and succeed, which have you done?
Perhaps you did substitute, but I see no dx, I see no integration. I see a trig equation and nothing more....
[=RoyalBlue][=Comic Sans MS]
"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," say Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It
please explain this
pianogirl2422 wrote:
udu = -udu
and this
pianogirl2422 wrote:
1/2 = cos^2x
cos^-1(1/2) = 2x
You know you're an AP student if...
you think studying is fun.
you constantly find yourself saying "we had homework?"
everything you know about sex, you learned in english class.
If you try to fail, and succeed, which have you done?
chessmaster1990 wrote:Take the integral of sinxcosx using substitution.
Substituting u:=sinx then du = cosxdx and you get the integral of udu = (sin^2x)/2
Substituting u:=cosx then du = -sinxdx and you get the integral of -udu = -(cos^2x)/2
here we go, integrate the same thing twice, get two solutions. if you integrate the same thing it should equal the same thing so.
chessmaster1990 wrote:
(sin^2x)/2 = -(cos^2x)/2
(1-cos^2x)/2 = -(cos^2x)/2
1/2 - (cos^2x)/2 = -(cos^2x)/2
1/2 = 0
1 = 0
Cool huh.
I don't see how I didn't integrate it...
You know you're an AP student if...
you think studying is fun.
you constantly find yourself saying "we had homework?"
everything you know about sex, you learned in english class.
If you try to fail, and succeed, which have you done?
Wow, I must be really tired...too many vectors.
Ok, so you're still flawed in logic.....
Where are your C's???
[=RoyalBlue][=Comic Sans MS]
"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," say Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It
well, obviously I'm flawed in logic somehow if I got 1=0. Points go to pianogirl for discovering the missing C. you really get
(sin^2x)/2 + C = -(cos^2x)/2 + C
(1-cos^2x)/2 + C = -(cos^2x)/2 + C
1/2 - (cos^2x)/2 + C = -(cos^2x)/2 + C
C = 1/2. Here is the follow up question. Now evaluate the definite integral from -pi/2 to pi/2. Cs will cancel out, what are we gonna do?!?
You know you're an AP student if...
you think studying is fun.
you constantly find yourself saying "we had homework?"
everything you know about sex, you learned in english class.
If you try to fail, and succeed, which have you done?
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