Is this part of the 2 unit course? (1 Viewer)

MrBrightside · Aug 11, 2011

Integral of xcos(x) dx ?

video: http://www.youtube.com/watch?v=Pra6r20geXU&feature=relmfu

SpiralFlex · Aug 11, 2011

MrBrightside said:
Integral of xcos(x) dx ?

video: http://www.youtube.com/watch?v=Pra6r20geXU&feature=relmfu

No. This is done in 4 Unit.

michaeljennings · Aug 11, 2011

integration by parts! yeah baby

MrBrightside · Aug 11, 2011

SpiralFlex said:
No. This is done in 4 Unit.

farrkin thank God. phew almost had a heart attack.

tambam · Aug 11, 2011

michaeljennings said:
integration by parts! yeah baby

$\int_{0}^{1}\frac{e^{cos^{-1}}x}{\sqrt{1-x^{2}}}dx$
Is this an integration by parts question?
I figured out how to do it, but i didn't realise that you could integrate them separately and then shove it back together....

michaeljennings · Aug 11, 2011

tambam said:
$\int_{0}^{1}\frac{e^{cos^{-1}}x}{\sqrt{1-x^{2}}}dx$
Is this an integration by parts question?
I figured out how to do it, but i didn't realise that you could integrate them separately and then shove it back together....

No this is a substitution question im fairly sure you get negative e to the power of inverse cos as your value you sub 1 and 0 into am i correct?

nightweaver066 · Aug 11, 2011

michaeljennings said:
No this is a substitution question im fairly sure you get negative e to the power of inverse cos as your value you sub 1 and 0 into am i correct?

Yes that's correct.

michaeljennings · Aug 11, 2011

nightweaver066 said:
Yes that's correct.

someone has to teach me how to write these things nicely like tambam idk how to do it

SpiralFlex · Aug 11, 2011

tambam said:
$\int_{0}^{1}\frac{e^{cos^{-1}}x}{\sqrt{1-x^{2}}}dx$
Is this an integration by parts question?
I figured out how to do it, but i didn't realise that you could integrate them separately and then shove it back together....

It can be easily integrated with substitution.

I will ignore the definite integral.

Let $u=\cos^{-1}x$

$du=-\frac{1}{\sqrt{\1-x^2}}\: \mathrm{d} x$

$-\int e^u * \frac{1}{\sqrt{1-x^2}} \: \mathrm{d} x$

$-\int e^u \: \mathrm{d} u$

$=-e^u + C$

$-e^\cos^{-1}x$ $\:+C$

tambam · Aug 11, 2011

michaeljennings said:
No this is a substitution question im fairly sure you get negative e to the power of inverse cos as your value you sub 1 and 0 into am i correct?

Whattt? lies. it was in the 2010 ext1 paper, and it did not say 'use the substitution blablablah' which is what substitution questions in ext 1 are meant to be.

michaeljennings · Aug 11, 2011

tambam said:
Whattt? lies. it was in the 2010 ext1 paper, and it did not say 'use the substitution blablablah' which is what substitution questions in ext 1 are meant to be.

was that our school paper?

tambam · Aug 11, 2011

michaeljennings said:
was that our school paper?

yeah, isn't ext1 integration by substitution meant to always give you the substitution?

michaeljennings · Aug 11, 2011

tambam said:
yeah, isn't ext1 integration by substitution meant to always give you the substitution?

yes it is hang on ill have a look at the paper

Is this part of the 2 unit course? (1 Viewer)

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