Integration

Dragonmaster262 · 7 Nov 2009, 11:58 PM

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Integrate:

f'(x) = (x^3)/(x+1)

Trebla · 8 Nov 2009, 12:04 AM

Dragonmaster262 · 8 Nov 2009, 12:08 AM

What's the general solution of Log e (sinx + cosx) + c?

tommykins · 8 Nov 2009, 3:53 AM

what do you mean the 'general solution'? doesn't make sense.

Dragonmaster262 · 8 Nov 2009, 8:23 AM

What domain can y exist in?

biopia · 8 Nov 2009, 9:08 AM

Well the domain for that function will be all real x minus wherever there are asymptotes.
i.e. everywhere except when sinx+cosx=0

If you restrict it, a possible answer for the domain may be -π/4 < x < 3π/4

Lol, now I get why you asked for the general solution :P Tbh, I don't know how I would express that, since it's a domain and not solutions to the equation.

I hope I helped in some way. Sorry if it didn't!
=]

7 Nov 2009, 11:58 PM	#1 (permalink)
Dragonmaster262 Executive Member HSC: 2010 Gender: Male Location: NSW Join Date: Jan 2009 Posts: 756 Last Activity: Today, 12:17 AM Blog Entries: 1	Integration You can hide this advertisement by registering. Integrate: f'(x) = (x^3)/(x+1) __________________ HSC 2010: Mathematics Ext 1 + Mathematics Ext 2 + Physics + Chemistry + Biology + English Advanced + Legal Studies PHS: Class of 2010 Need any Free Past Papers for Sciences and Maths? Please PM me with your e-mail address and I'll see what I can do. Please be specific with which papers you want otherwise your PM will be ignored.

8 Nov 2009, 12:04 AM	#2 (permalink)
Trebla Loquacious One HSC: 2006 Gender: Male Join Date: Feb 2005 Posts: 2,220 Last Activity: Today, 1:38 AM	Re: Integration $\dfrac{x^3}{x+1}=\dfrac{x^3+1-1}{x+1}\\\\=\dfrac{(x+1)(x^2-x+1)}{x+1}-\dfrac{1}{x+1}\\\\= x^2-x+1-\dfrac{1}{x+1}\\\\\therefore f'(x)=x^2-x+1-\dfrac{1}{x+1}\\\\\Rightarrow f(x)= \dfrac{x^3}{3}-\dfrac{x^2}{2}+x-\ln (x+1)+c$ __________________ Tutor available for: - Mathematics (HSC and Preliminary) - Mathematics Extension 1 (HSC and Preliminary) - Mathematics Extension 2 For further details: http://community.boredofstudies.org/...85#post4611085

8 Nov 2009, 12:08 AM	#3 (permalink)
Dragonmaster262 Executive Member HSC: 2010 Gender: Male Location: NSW Join Date: Jan 2009 Posts: 756 Last Activity: Today, 12:17 AM Blog Entries: 1	Re: Integration What's the general solution of Log e (sinx + cosx) + c? __________________ HSC 2010: Mathematics Ext 1 + Mathematics Ext 2 + Physics + Chemistry + Biology + English Advanced + Legal Studies PHS: Class of 2010 Need any Free Past Papers for Sciences and Maths? Please PM me with your e-mail address and I'll see what I can do. Please be specific with which papers you want otherwise your PM will be ignored.

8 Nov 2009, 3:53 AM	#4 (permalink)
tommykins i am number -e^i*pi HSC: 2008 Gender: Male Join Date: Feb 2007 Posts: 4,671 Last Activity: Today, 2:12 AM	Re: Integration what do you mean the 'general solution'? doesn't make sense. __________________ \|3 C1\/1\|_ 3/\/G1/\/33\|21/\/G @ \|_\|/\/5\/\/ I

8 Nov 2009, 8:23 AM	#5 (permalink)
Dragonmaster262 Executive Member HSC: 2010 Gender: Male Location: NSW Join Date: Jan 2009 Posts: 756 Last Activity: Today, 12:17 AM Blog Entries: 1	Re: Integration What domain can y exist in? __________________ HSC 2010: Mathematics Ext 1 + Mathematics Ext 2 + Physics + Chemistry + Biology + English Advanced + Legal Studies PHS: Class of 2010 Need any Free Past Papers for Sciences and Maths? Please PM me with your e-mail address and I'll see what I can do. Please be specific with which papers you want otherwise your PM will be ignored.

8 Nov 2009, 9:08 AM	#6 (permalink)
biopia DONE! :D HSC: 2009 Gender: Male Join Date: Nov 2008 Posts: 96 Last Activity: Today, 3:18 AM	Re: Integration Well the domain for that function will be all real x minus wherever there are asymptotes. i.e. everywhere except when sinx+cosx=0 If you restrict it, a possible answer for the domain may be -π/4 < x < 3π/4 Lol, now I get why you asked for the general solution :P Tbh, I don't know how I would express that, since it's a domain and not solutions to the equation. I hope I helped in some way. Sorry if it didn't! =] __________________ Updated Ranks [Rank Order Notice] EngAdv (3/55) \| MX1 (1/5) \| MX2 (1/4) \| Mus1 (1/17) \| Physics (1/14) \| Photo (1/12) Now that I am DONE, I need no expectations. Whatever will be will be, and I will be happy with whatever I get ATAR Needed: 94.45 [Bachelor of Design in Architecture, University of Sydney] ATAR Wanted: 97.20+ Last edited by biopia; 8 Nov 2009 at 5:12 PM.

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