Shadowless
Member
- Joined
- May 3, 2010
- Messages
- 342
- Gender
- Male
- HSC
- 2012
Re: MX2 Integration Marathon
How do u get those integral symbols
How do u get those integral symbols
-
Best of luck to the class of 2025 for their HSC exams. You got this! Let us know your thoughts on the HSC exams here
HSC 2012-14 MX2 Integration Marathon (archive) (2 Viewers)
- Thread starter bleakarcher
- Start date
- Status
rolpsy
Member
- Joined
- Apr 9, 2011
- Messages
- 94
- Gender
- Male
- HSC
- 2012
Re: MX2 Integration Marathon
yup
Now IIRC, that second integral is easily done by 2 applications of IBP and rearrangements.
D: i just realised its undefined at x = 0.. L'Hopital's rule?
SpiralFlex
Well-Known Member
- Joined
- Dec 18, 2010
- Messages
- 6,954
- Gender
- Female
- HSC
- N/A
Re: MX2 Integration Marathon
ill have a go at ur soon! once i finish studying for mx1.
lol forgot to integrate, thank u, i fixed itlol you forgot to integrate!
which gives the correct answer
here is a really difficult one:
good luck
ill have a go at ur soon! once i finish studying for mx1.
seanieg89
Well-Known Member
- Joined
- Aug 8, 2006
- Messages
- 2,653
- Gender
- Male
- HSC
- 2007
Re: MX2 Integration Marathon
U MAD BRO keep your integrals at the level of the MX2 integration topic. If you are interested in how to do these yourself, do outside research / ask in extracurricular. This thread is an inappropriate place to post them.
@Rolpsy nice question!
\,dx=\int_0^{\pi/2}(\pi/2-x)\tan(x)\,dx\\ \Rightarrow 2I=\int_0^{\pi/2}\frac{2x\cos^2(x)+2(\pi/2-x)\sin^2(x)}{2\sin(x)\cos(x)}\, dx\\=\int_0^{\pi/2}\frac{2x\cos(2x)+\frac{\pi}{2}(1-\cos(2x))}{\sin(2x)}\,dx\\\Rightarrow 4I=\int_0^{\pi}\frac{x\cos(x)+\frac{\pi}{2}(1-\cos(x))}{\sin(x)}\, dx\\=\int_0^{\pi/2}x\cot(x)\,dx+\frac{\pi}{2}\int_0^{\pi/2}\csc(x)-\cot(x)\,dx+\int_{\pi/2}^\pi (x-\pi)\cot(x)\,dx+\frac{\pi}{2}\int_{\pi/2}^\pi\csc(x)+\cot(x)\,dx\\=2I+\pi\int_0^{\pi/2}\csc(x)-\cot(x)\,dx\\=2I-\pi\log|1+\cos(x)|]^{\pi/2}_0\\\Rightarrow I=\frac{\pi}{2}\log(2).)
U MAD BRO keep your integrals at the level of the MX2 integration topic. If you are interested in how to do these yourself, do outside research / ask in extracurricular. This thread is an inappropriate place to post them.
@Rolpsy nice question!
Johnstan
Sickunt overload
Re: MX2 Integration Marathon
best be getting involved brahFuuark this thread looks so interesting. Will get involved soon
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,467
- Gender
- Undisclosed
- HSC
- N/A
Re: MX2 Integration Marathon
You will never be asked straight out to evaluate special integrals like the Logarithmic, Sine, Gaussian Integrals all in one go. If anything, they will lead you into it.
You will never be asked straight out to evaluate special integrals like the Logarithmic, Sine, Gaussian Integrals all in one go. If anything, they will lead you into it.
Last edited:
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,467
- Gender
- Undisclosed
- HSC
- N/A
Re: MX2 Integration Marathon
In which case, a Cauchy Principle Value is assigned.
But like seanieg89 said, try to keep your integrals relatively elementary in nature.
Sometimes, numerical values are assigned to integrals that would otherwise have no value because the domain of integration contains a point of singularity or a discontinuity.
In which case, a Cauchy Principle Value is assigned.
But like seanieg89 said, try to keep your integrals relatively elementary in nature.
Re: MX2 Integration Marathon
I'm really interested to know how to do these integrals, I'll post them in extracurricular =)
- Status