Parenthesis is best, because otherwise it's ambiguous. It could be understood as 5*cos(8)*x^5 - 200*(x^5)*sin(8)*(x^5) without the parenthesis. For number 1, including the c is the most mathematically correct, assuming that C is a constant; but because the problem says "a function," then I suppose you could plug in any constant into C, including 0.

Raithed

China7078 Posts

October 24 2008 04:32 GMT

#23

yeah also i always get this confused and i dont really know how to explain it, like you would have to rewrite sin8x or whatever... uh.. i dont know how to explain it, bah nevermind.

Zortch

Canada635 Posts

October 24 2008 04:34 GMT

#24

On October 24 2008 12:23 HnR)Insane wrote:
http://integrals.wolfram.com/index.jsp
Just use that if you need to check your integration answers.

ed: I realize you're finding derivatives btw, but you can still use it to check your answers.
ed2: I realize also that micronesia suggested something like that before, but I provided an actual link

Check your answer for 2 using this ^.

Raithed

China7078 Posts

October 24 2008 04:35 GMT

#25

number 2? but number 2 isnt integral you mean 1? =P

Descent

1244 Posts

October 24 2008 04:37 GMT

#26

http://integrals.wolfram.com/index.jsp?expr=(.5)(6-x^2)(x^(-1/2))(x^2+6)^((-3/2))&random=false

Zortch

Canada635 Posts

October 24 2008 04:38 GMT

#27

I mean 2. Put in your answer, and see if you get the question back heh.
That program find the anti-derivative(or indefinite integral) of the derivative you found

Raithed

China7078 Posts

October 24 2008 04:46 GMT

#28

oh wow, i just noticed that my answer is wrong since descent inputted a -(3/2) my answer is 3/2...?

Descent

1244 Posts

October 24 2008 04:50 GMT

#29

On October 24 2008 13:46 Raithed wrote:
oh wow, i just noticed that my answer is wrong since descent inputted a -(3/2) my answer is 3/2...?

Our answers are the same. Your (x^2+6) is in the denominator, but mine is in the numerator, so they are the same.

Raithed

China7078 Posts

October 24 2008 04:55 GMT

#30

okay i was about to say haha, the more i look into it the more i keep thinking its wrong. uhmmm. so typed, this is okay or should i have a parenthesis governing the denom?

Descent

1244 Posts

October 24 2008 05:04 GMT

#31

It looks completely comprehensible to me. To be super safe, you might want to put the (6-x^2) in parenthesis, but it's completely unnecessary.

...I will feel very silly if it turns out to be incorrect. =<

Raithed

China7078 Posts

October 24 2008 05:13 GMT

#32

yeah i just want it to be good. sorry for backtracking but lets go back to number 1. if it was just an S(integral) sign then i would reall nderstand it to be +C but this really didnt give me 0 to 4, so i can only assume its an indefinite integral so its answer + C right? i just really want to make sure because i dont want to do any silly mistakes.

Descent

1244 Posts

October 24 2008 05:23 GMT

#33

The most correct general solution includes the C constant, with the acknowledgment that C is only a constant (and not some function). I think it should be included, but I also have to concur with Zortch in that the wording of the problem is "a function," meaning that any C is acceptable. This would include 0, in which case you wouldn't need to write it at all. I think it should be included for completeness, but I doubt it matters (to clarify, I don't think that the problem really seems to care whether or not you include it, based on its wording).