Calculus HELP!!!

[BoneStockHonda]

Hey guys I need help with a problem. I have to integrate:

(k^2)*sin(πx/2k)

(The symbol before the x is suppose to be Pi)

I know k^2 would come out to (k^3)/3, but what would the rest of the problem be. ( yes I know I have to plug in my numbers to integrate but I can't get to that point)

THANKS!
-Matt

[atvfrk10]

Are you integrating with respect to "k" or "x"? or is it a double integral?

[BoneStockHonda]

I have to solve to for K. I'll post up a picture of the problem give me a second.

[BoneStockHonda]

Here it is:

[atvfrk10]

Well, essentially "K" is just a constant and because it is a constant is can be pulled out of the integral.

The "1/(k-0)" is of course "1/k" so then the "k^2" is pulled out it just becomes "k" multiplied by the integral.

With the "k^2" pulled out, the integral becomes

sin( ( pi*x ) / (2*k)).

So you just take the integral of that function from 0 to K

To do that you do what called u substitution
where

u = pi/(2*k)

so the integral becomes sin(u*x)

integrate that and it becomes

-1/u * cos(u*x)

plug the "u" back in and you get

-(2*k)/pi * cos ( (pi*x) / (2*k))

plug the integrands into the equation for the "x"

so it becomes -(2*k)/pi * cos ( (pi*k) / (2*k)) - (-(2*k)/pi * cos ( (pi*0) / (2*k))

which ultimately simplified to

-(2*k)/pi * cos ( (pi*k) / (2*k)) + 2k/pi

multiply the whole thing by the "k" that was outside the integral and solve!

hopefully that helps.

Now, do you want to help me with my fracture mechanics homework? ;)

[BoneStockHonda]

Thanks a lot man! This can seriously be the difference between me passing or failing the semester. I missed the entire unit of integration because I was out of school due to injury so I'm really struggling now. And I'll take a rain check on fracture mechanics lol.

[atvfrk10]

no problem man. Best of luck to you!

[wilkin250r]

Man, if you're not sure about u substitution, you need SERIOUS help to finish this class. No joke, you're probably going to need four or five tutoring sessions just to get caught up.

[dns1764]

i cant do u substitution and i made my way up to cal 3. remember buddy, d's get degrees!!

[wilkin250r]

Originally posted by dns1764
i cant do u substitution and i made my way up to cal 3. remember buddy, d's get degrees!!

and I can't do a U substitution like the one posted above, that one is different than anything I've ever learned.

[BoneStockHonda]

I'm working on it I've been staying after to try to catch up

[derekhonda]

I liked calculus so much I took it three times!