Calculus gurus

[Rockman]

I'm sure you exist on this forum, I need some help. How should I go about integrating this: cos(x)/sin(x)^5

[TrooperFarva]

What is to the 5th power, just sin?

What are the limits?

[Chebass88]

Originally Posted by Rockman

I'm sure you exist on this forum, I need some help. How should I go about integrating this: cos(x)/sin(x)^5

Do a "u substitution".

Steps to take:
1. Let u = sin(x)
2. Find du (du = cos(x)dx
3. Substitute u & du into original integral to obtain:

integral of (du / (u^5)), which should be:

-4*u^-4 + C, where C is the constant of integration. At this point you'd use the limits of integration (if supplied), if not, that answer is complete.

Q.E.D.

ian

[Rockman]

Originally Posted by Chebass88

Do a "u substitution".

Steps to take:
1. Let u = sin(x)
2. Find du (du = cos(x)dx
3. Substitute u & du into original integral to obtain:

integral of (du / (u^5)), which should be:

-4*u^-4 + C, where C is the constant of integration. At this point you'd use the limits of integration (if supplied), if not, that answer is complete.

Q.E.D.

ian

Wouldn't the integral be -1/(4u^4)?

[fdeck]

Originally Posted by Chebass88

Do a "u substitution".

Steps to take:
1. Let u = sin(x)
2. Find du (du = cos(x)dx
3. Substitute u & du into original integral to obtain:

integral of (du / (u^5)), which should be:

-4*u^-4 + C, where C is the constant of integration. At this point you'd use the limits of integration (if supplied), if not, that answer is complete.

Q.E.D.

ian

Nice.

In general, if one part of the integrand looks like the derivative of another part, it's worth seeing if substitution works. To the OP, make sure you know your basic derivatives down cold.

[Simo98]

I just had a test on this...

..i dont think i did very well xP

[Absentia]

Start
run
calc
enter


hell I can't even count my toes good luck to ya

[Rockman]

Originally Posted by fdeck

Nice.

In general, if one part of the integrand looks like the derivative of another part, it's worth seeing if substitution works. To the OP, make sure you know your basic derivatives down cold.

He thanks, I wish my TA could make statements that were actually helpful to teach. I guess I was just rusty after a summer of not doing calc, they are going better now. Thank god, otherwise it would have been a loooon semester.

[fdeck]

I wouldn't say this about any other math class, but a fair portion of calculus is what one might call "tricks." But really it is more than that. You are learning to recognize the "form" of expressions, and how you can manipulate each form, much in the same way that a musician learns how to work with different structures of chords.

[Chebass88]

Originally Posted by Rockman

Wouldn't the integral be -1/(4u^4)?

With the exception of the 4 in the denominator, our expressions are equivalent. x^-n = 1/x^n.

This is using the general form: derivative of x^n = n*x^n-1, where of course n =/= 0.

ian

[B.C.]

Originally Posted by fdeck

Nice.

In general, if one part of the integrand looks like the derivative of another part, it's worth seeing if substitution works. To the OP, make sure you know your basic derivatives down cold.

Absolutely correct

Originally Posted by fdeck

I wouldn't say this about any other math class, but a fair portion of calculus is what one might call "tricks." But really it is more than that. You are learning to recognize the "form" of expressions, and how you can manipulate each form, much in the same way that a musician learns how to work with different structures of chords.

Never thought about it that way, but looking at it, you are absolutely correct.

[Fontaine]

i did that last year in college, i already pressed the delete button on that one, sorry.

[fdeck]

Originally Posted by B.C.

Absolutely correct + C

Fixed it for you.

[Rockman]

Really this is going to put a damper on my plans. Its so frustrating, I get to a point where its all set to go, and I just can't make it happen.

[B.C.]

Originally Posted by fdeck

Fixed it for you.

I see Watt you did there

Originally Posted by Rockman

Really this is going to put a damper on my plans. Its so frustrating, I get to a point where its all set to go, and I just can't make it happen.

How so?

[fdeck]

Originally Posted by Rockman

Really this is going to put a damper on my plans. Its so frustrating, I get to a point where its all set to go, and I just can't make it happen.

Is it too late to change teachers? If not, the next best thing may be to form or find a study group.

[Rockman]

Originally Posted by fdeck

Is it too late to change teachers? If not, the next best thing may be to form or find a study group.

No its not, but an email was sent today. I think its better if I just copy and paste.

Dear Professor Boyle,

I thought it would be a good idea if you e-mailed all the students about how to
type the answers to the indefinite integrals. I had number 10 marked incorrect a
friend told me I had to type the constant in as a capital C. Hope this will help
others, and thank you for your time.


Sarah Yang

Needless to say this explains those 4 problems that I got wrong which I knew were right.

[Chebass88]

You should begin calling the constant "Q", just to throw a mathematical monkey wrench into the mix.