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Edexcel A2 C4 Mathematics June 2015 - Official Thread

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Use U=cosx, and you should be good

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Original post by arsenalfc97
When finding the shortest distance from the point to a line, how can you assume that a right angle is made between the point and the line?


Draw a line and draw a point. Draw random connections from that point to the line. You will bee the shortest distance is when the connection is perpendicular to the line
Hey can someone please explain to me June 2014, 7b and how the volume of a cone thing works- don't get it
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mb_12
1
Original post by manlikem
what do you mean? The question is just integrate sinx cos^3 x dx


The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
Integral of cos^3x
= integral of cosx cos^2x
= integral of cosx (1 - sin^2x)
= integral of cosx - cosx sin^2x
Then use integration of even powers of sinx
Hope it helps
https://5a302d29ff432793ce79475dd3dba997851918fc.googledrive.com/host/0B1ZiqBksUHNYNElsMEE2MDU0eWM/12%20Gold%202%20-%20C4%20Edexcel.pdf

how do you do Question 4?
nvm
(edited 8 years ago)
Original post by manlikem
untitled.JPG


You cant do it by parts, as i keep going in loops and circles haha. I think you do it by inspection? which is something i cant do, but will have another try :biggrin:
Do we have to use the identical to sign when writing partial fractions or can we just use the '=' sign? Would we lose marks
If you ever have any integral involving both sine and cosine functions in C4, you can hazard a guess that some kind of substitution will be involved, seeing as one derives the other (more or less).
Can anyone explain question 8F from the IAL January 2014 paper (link: http://www.physicsandmathstutor.com/a-level-maths-papers/c4-edexcel/ )
Thank you ^.^
(edited 8 years ago)
:smile:
Original post by sj97



Original post by SeanFM
Well, you've expanded 8-9x cube rooted, and you're asked to find the cube root of 7100. So you ask yourself how you can make 8-9x look anything like 7100. Well, x=1/10 makes it 7.1, so using the expansion you get the cube root of 7.1. But we want the cube root of something a thousand times bigger.

Just like (2*4)^2 = 8^2 = 64 = 4*16 = 2^2 * 4^2, the cube root of 7100 can be split into the cube root of 7.1 and the cube root of 1000 multiplied together. So you get the expansion for 7.1 and multiply by the cube root of 1000, which is 10.
(edited 8 years ago)
Original post by frozo123


First, separate the functions of the variables yy and xx and in doing so integrate both sides; remember:

dydx=f(x)g(y)  ⟹  ∫1g(y)dy=∫f(x)dx\dfrac{dy}{dx} = f(x)g(y) \implies \displaystyle\int \dfrac{1}{g(y)} dy = \displaystyle\int f(x) dx
Original post by mb_12
The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
Integral of cos^3x
= integral of cosx cos^2x
= integral of cosx (1 - sin^2x)
= integral of cosx - cosx sin^2x
Then use integration of even powers of sinx
Hope it helps


So what what would you do exactly after you get cosx - cosx sin^2x ??
EDIT: Ignore, lol.
(edited 8 years ago)
Original post by mb_12
The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
Integral of cos^3x
= integral of cosx cos^2x
= integral of cosx (1 - sin^2x)
= integral of cosx - cosx sin^2x
Then use integration of even powers of sinx
Hope it helps


I think even then that is perhaps a little complicated; consider instead:

∫cos⁡3(x)dx=∫cos⁡(x)(1−sin⁡2(x))dx\displaystyle\int \cos^3(x) dx = \displaystyle\int \cos(x)(1 - \sin^2(x)) dx, then, substitute u(x):=sin⁡(x)u(x) := \sin(x).

Although I am aware that the original question was to integrate a function of both sine and cosine, the above hopefully illustrates how to integrate an odd power of cosine (/sine).
(edited 8 years ago)
Original post by Paraphilos
First, separate the functions of the variables yy and xx and in doing so integrate both sides; remember:

dydx=f(x)g(y)  ⟹  ∫1g(y)dy=∫f(x)dx\dfrac{dy}{dx} = f(x)g(y) \implies \displaystyle\int \dfrac{1}{g(y)} dy = \displaystyle\int f(x) dx


is it y=2(e^tan3x+1)?
Original post by mb_12
The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
Integral of cos^3x
= integral of cosx cos^2x
= integral of cosx (1 - sin^2x)
= integral of cosx - cosx sin^2x
Then use integration of even powers of sinx
Hope it helps


thanks! and if I use substitution could I make cos x = u?
Original post by Alice Moody
You cant do it by parts, as i keep going in loops and circles haha. I think you do it by inspection? which is something i cant do, but will have another try :biggrin:


thanks for trying!
Hopefully vectors aint the last question, when it is its usually a mad ting


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Original post by manlikem
thanks! and if I use substitution could I make cos x = u?


See my post above.
Original post by manlikem
untitled.JPG


Think ive got an answer!!
cos^4x --> integrate this --> -4sinxcos^3x
You want sinxcos^3x, so just divide by 4 to give -1/4cos^4x+c

Hope this helps!!

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