Edexcel A2 C4 Mathematics June 2015 - Official Thread

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$\int 2sin^{2}x\cdot cosx\, dx$
What would be most efficient/intuitive way to integrate this? It came up in an Edexcel paper and they didn't give any information on which method to use, and in the mark scheme they didn't even show the steps for intergrating it.

Recongnition

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Reply 821

tflanjee

u=sinx
du/dx=cosx
dx=du/cosx
so the integral turns to 2u^2 as the cosx cancels out.
No limits to change
So the integral is 2/3 u^3
which is 2/3 sin^3x

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Reply 822

username1162972

Original post by lam12

Recognition, any tips then what to look out for in order to do it?

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Look at the differntial of each funcion. Consider the power to a higher power. Then divide by this new power and add a minus sign if needed

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Reply 823

tflanjee

If you've got two lines, one with the gradient 1 and the other with the gradient 1/3, how is this the gradient between them?

Reply 824

tflanjee

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question 3.PNG

Reply 825

Elliemay97

Hi can anyone help me with part a? I'm a bit confused on what the the question is asking you to do?

Reply 826

LMottram

Helloooo!
Do you needs to know the proofs for:
a.b = b.a
and
a.(b + c) = a.b + a.c

It's in my text book but I don't know if we have to be able to fully recall it?
Thanks!

Reply 827

Medicjug

Original post by LMottram

Helloooo!
Do you needs to know the proofs for:
a.b = b.a
and
a.(b + c) = a.b + a.c

It's in my text book but I don't know if we have to be able to fully recall it?
Thanks!

I'm pretty sure you don't need to know it

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Reply 828

username1194059

Original post by Elliemay97

Hi can anyone help me with part a? I'm a bit confused on what the the question is asking you to do?

Its just asking how you'd set up the integral. So to find the area of R you'd need to use ∫y.dx/dt. Which will then get you to the answer it wants you to show.

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Reply 829

Medicjug

Original post by ooftar

Its just asking how you'd set up the integral. So to find the area of R you'd need to use ∫y.dx/dt. Which will then get you to the answer it wants you to show.

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First mark is for saying r= integral of y dx
Then differentiate x and find what dt is. Put it in and simplify.

Change the bounds too

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cant do b

Original post by Yua

cant do b

When x=0 g(x)=3 look at the graph 3>g(x)>0

Reply 832

Wahid1

Original post by skyakdu

But g(x) can never go below 1/2 as x tends to infinity so it'd be 3 >= g(x) > 1/2

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Wrong thread

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Reply 833

NightAl96

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