Calculus is being difficult.

Phoenix Down

Phoenix Down

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3w?
Okay so... after 2 hours of staring this is what i have


I know if I just keep reducing, I'll get a good answer.
But... I can't help but think. THERE HAS TO BE AN EASIER FASTER MORE ELOQUENT WAY TO SOLVE THIS. Any ideas?
 
yea I dropped this class.
but d00d
I always ask math questions to yahoo answers. When I'm not asking about my relationships and/or teen pregnancy
 
All I can think of is this.
k8y.jpg

I always get bugged by problems like that too, looking for a simpler way. Try solving a simper problem (using perfect squares, not using sines, etc.)
 
nope as far as i have gone in calc you have to expand it all the way out...

HAVE FUN!
 
I used to know how to do stuff like that. Then I hit my head and lost consciousness on two occasions. Then I aged. Then I stopped caring.

Sorry. I hope someone can help.
 
Ok.

Change both your sin^2(x) and cos^2(x) into their repespective half angles: (1/2)(1-cos(2x))(1/2)(1+cos(2x))
Now pull out the 1/4 in front of your integral and expand the terms inside the integral
As you can see you have to do the half angle formula again.
After cleaning things up a bit, you will see that you have 2 simple integrals, 1 power rule, and one Known

If you have any questions, ask :)
 
Serenity said:
Ok.

Change both your sin^2(x) and cos^2(x) into their repespective half angles: (1/2)(1-cos(2x))(1/2)(1+cos(2x))
Now pull out the 1/4 in front of your integral and expand the terms inside the integral
As you can see you have to do the half angle formula again.
After cleaning things up a bit, you will see that you have 2 simple integrals, 1 power rule, and one Known

If you have any questions, ask :)
Click to expand...

That seems right because what the OP was doing doesn't look entirely correct but I haven't worked on integral laws in a while.
 
Phoenix Down said:
Okay so... after 2 hours of staring this is what i have


I know if I just keep reducing, I'll get a good answer.
But... I can't help but think. THERE HAS TO BE AN EASIER FASTER MORE ELOQUENT WAY TO SOLVE THIS. Any ideas?
Click to expand...

I don't know! :m028:
 
Ok, I looked this up on wolframalpha.com and this problem is definitely a bitch. There are literally 20 steps (including parts, f that) and the answer it gave me was...

(1/32)(4x-sin(4x)) + constant
 
After 2 seconds of staring this is what I have:

Start by simplifying into (sin[x]cos[x])^2 = (0.5sin[2x])^2,
and you know what to do from there.

Anyone: let me know if you have maths problems. :D

edit: actually whytiger got to this a few minutes before i did. Serenity's is similar
 
Last edited:
Artsu Tharaz said:
After 2 seconds of staring this is what I have:

Start by simplifying into (sin[x]cos[x])^2 = (0.5sin[2x])^2,
and you know what to do from there.

Anyone: let me know if you have maths problems. :D
Click to expand...

Well, this isn't right.

Integral of Cos(x)Sin(x)= -.5Cos^2(x) but we're trying to find the Integral of (Cos(x)Sin(x))^2 which turns out to be...

(1/32)(4x-sin(4x)) + Constant

That is the answer, no arguments. I'm sorry.
 
bickelz said:
Well, this isn't right.

Integral of Cos(x)Sin(x)= -.5Cos^2(x) but we're trying to find the Integral of (Cos(x)Sin(x))^2 which turns out to be...

(1/32)(4x-sin(4x)) + Constant

That is the answer, no arguments. I'm sorry.
Click to expand...

-_o

To start with, bickelz.

Then you transform that using the double angle result for cosine, which the OP clearly knows how to do,
And then it's a very simple integral (except for the pesky constants) to get the solution you have there.
 
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