HSC 2016 MX2 Integration Marathon (archive) (1 Viewer)

math man · Apr 24, 2016

Re: MX2 2016 Integration Marathon

Paradoxica said:
.

That was my 2nd fav in that list of 4

Paradoxica · Apr 24, 2016

Re: MX2 2016 Integration Marathon

math man said:
That was my 2nd fav in that list of 4

well I'm not posting anymore until all integrals are finished. So far, only one of the four are complete.

math man · Apr 24, 2016

Re: MX2 2016 Integration Marathon

Paradoxica said:
well I'm not posting anymore until all integrals are finished. So far, only one of the four are complete.

Just have to wait till the actually HSC students do them then!

Nailgun · Apr 24, 2016

Re: MX2 2016 Integration Marathon

have i mentioned that maths kids are a bit egotistical

Paradoxica · Apr 24, 2016

Re: MX2 2016 Integration Marathon

Nailgun said:
have i mentioned that maths kids are a bit egotistical

Your point being ???...

KingOfActing · Apr 24, 2016

Re: MX2 2016 Integration Marathon

Nailgun said:
have i mentioned that maths kids are a bit egotistical

I try not to be

Paradoxica · Apr 27, 2016

Re: MX2 2016 Integration Marathon

Paradoxica said:
$\int \frac{\sum_{r=0}^{n}\sin{rx}}{\sum_{r=0}^{n}\cos{rx}}\,$d$x$

Never answered lol

Paradoxica · Apr 30, 2016

Re: MX2 2016 Integration Marathon

$I = \int_0^1 \frac{x^4(1-x^2)^5}{(1+x^2)^{10}}$d$x$

$$Find $\frac{1}{I}$

Paradoxica · Apr 30, 2016

Re: MX2 2016 Integration Marathon

$\int_0^\frac{\pi}{2} \frac{x\sin{x}\cos{x}}{(a^2\cos^2{x}+b^2\sin^2{x})^2}$d$x = \frac{\pi}{R}$

$$Find $R$

math man · Apr 30, 2016

Re: MX2 2016 Integration Marathon

Where do you find these integrals? Like I've seen these types before, but where are they from?

Paradoxica · Apr 30, 2016

Re: MX2 2016 Integration Marathon

math man said:
Where do you find these integrals? Like I've seen these types before, but where are they from?

That's my secret.

leehuan · Apr 30, 2016

Re: MX2 2016 Integration Marathon

Average difficulty question

$\int_0^4{\sqrt{x}\sqrt{x\sqrt{x}+1}dx}$

Paradoxica · Apr 30, 2016

Re: MX2 2016 Integration Marathon

leehuan said:
Average difficulty question

$\int_0^4{\sqrt{x}\sqrt{x\sqrt{x}+1}dx}$

104/9 by virtue of multiple reverse chains.

Paradoxica · May 8, 2016

Re: MX2 2016 Integration Marathon

$\noindent Evaluate $\int \frac{\text{d}x}{\sqrt{x^2 \pm k}}\\$a) In two ways, by multiplying it by $\frac{f(x)}{f(x)}$ where $f$ is one of two appropriate irrational functions.$\\$b) By using two different appropriate irrational substitutions.$

InteGrand · May 11, 2016

Re: MX2 2016 Integration Marathon

$\noindent Find $\int _0 ^{2\pi} \frac{x \cos x}{1 + \sin^2 x} \text{ d}x$.$

leehuan · May 11, 2016

Re: MX2 2016 Integration Marathon

InteGrand said:
$\noindent Find $\int _0 ^{2\pi} \frac{x \cos x}{1 + \sin^2 x} \text{ d}x$.$

Lol where have I seen this before

Drongoski · May 11, 2016

Re: MX2 2016 Integration Marathon

InteGrand said:
$\noindent Find $\int _0 ^{2\pi} \frac{x \cos x}{1 + \sin^2 x} \text{ d}x$.$

= 0

leehuan · May 11, 2016

Re: MX2 2016 Integration Marathon

Just to briefly sketch out InteGrand's question for anyone interested...

(Subject to inaccuracy)

$I=\int _{ 0 }^{ 2\pi }{ \frac { x\cos { x } }{ 1+\sin ^{ 2 }{ x } } dx } \\ =\int _{ 0 }^{ 2\pi }{ \frac { \left( 2\pi -x \right) \cos { \left( 2\pi -x \right) } }{ 1+\sin ^{ 2 }{ \left( 2\pi -x \right) } } dx } \\ =2\pi \int _{ 0 }^{ 2\pi }{ \frac { \cos { x } }{ 1+\sin ^{ 2 }{ x } } dx } -\int _{ 0 }^{ 2\pi }{ \frac { x\cos { x } }{ 1+\sin ^{ 2 }{ x } } dx } \\ =2\pi \int _{ 0 }^{ 2\pi }{ \frac { \cos { x } }{ 1+\sin ^{ 2 }{ x } } dx } -I\\ \therefore 2I=2\pi \int _{ 0 }^{ 2\pi }{ \frac { \cos { x } }{ 1+\sin ^{ 2 }{ x } } dx } \\ u=\sin { x } \Rightarrow du=\cos { x } dx\\ \sin { 0 } =\sin { 2\pi } =0\\ I=\pi \int _{ 0 }^{ 0 }{ \frac { du }{ 1+{ u }^{ 2 } } } \\ I=0$

leehuan · May 12, 2016

Re: MX2 2016 Integration Marathon

2014 HSC very last question

$\int{\frac{\ln{x}}{{(1+\ln{x})}^2}}dx$

DatAtarLyfe · May 12, 2016

Re: MX2 2016 Integration Marathon

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