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C3 Trig - Tricky?!

please help:

integral of sinx^2 cosx

Thanks

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what is ddx(sinx)\frac{d}{dx}(sinx) ?
Reply 2
Avatar for asem93
asem93
OP
Original post by TimmonaPortella
what is ddx(sinx)\frac{d}{dx}(sinx) ?


cosx
Original post by asem93
cosx


so, what substitution do you think you should make?
Reply 4
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asem93
OP
Original post by TimmonaPortella
so, what substitution do you think you should make?


u = sin x
du/dx = cos x
Original post by asem93
u = sin x
du/dx = cos x


:congrats::borat:
Reply 6
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asem93
OP
Original post by TimmonaPortella
:congrats::borat:


lol, I know that

but what after...
To clarify, is that sin(x2)sin(x^2) or (sinx)2(sinx)^2?
Then I'll take you through the first steps and see if you can go from there.
Original post by TimmonaPortella
To clarify, is that sin(x2)sin(x^2) or (sinx)2(sinx)^2?
Then I'll take you through the first steps and see if you can go from there.


I'm sure you know that the former option would not be Core 3.
Reply 9
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asem93
OP
Original post by TimmonaPortella
To clarify, is that sin(x2)sin(x^2) or (sinx)2(sinx)^2?
Then I'll take you through the first steps and see if you can go from there.


it is (sinx)2(sinx)^2
Original post by asem93
it is (sinx)2(sinx)^2


In future, call it sin⁡2x\sin^2 x as this notation avoids any confusion.
Reply 11
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asem93
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Original post by Mr M
In future, call it sin⁡2x\sin^2 x as this notation avoids any confusion.


Yes, sorry.
Original post by asem93
Yes, sorry.


You don't need to be sorry! Anyway, what does the substitution u = sin x transform your integral into?

Edit: I'm wondering if the fact that you have forgotten to include dx at the end of your integral is causing you a problem.
(edited 13 years ago)
Reply 13
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asem93
OP
Original post by Mr M
You don't need to be sorry! Anyway, what does the substitution u = sin x transform your integral into?


What do you mean transform? is that the integral of u^2 cosx
Reply 14
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asem93
OP
Original post by Mr M
You don't need to be sorry! Anyway, what does the substitution u = sin x transform your integral into?

Edit: I'm wondering if the fact that you have forgotten to include dx at the end of your integral is causing you a problem.


Ah I see.. I did forget it's dx... but what is the significance of that anyway?
Original post by asem93
What do you mean transform? is that the integral of u^2 cosx


Ok that is definitely your problem.

u=sin⁡xu=\sin x

du=cos⁡x dxdu = \cos x \, dx

∫sin⁡2xcos⁡x dx=∫u2 du\int \sin^2 x \cos x \, dx = \int u^2 \, du
Original post by asem93
Ah I see.. I did forget it's dx... but what is the significance of that anyway?


Have you been taught integration by substitution yet?
Reply 17
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asem93
OP
Original post by Mr M
Ok that is definitely your problem.

u=sin⁡xu=\sin x

du=cos⁡x dxdu = \cos x \, dx

∫sin⁡2xcos⁡x dx=∫u2 du\int \sin^2 x \cos x \, dx = \int u^2 \, du



Okay so the integral of u^2 is u^3/3 but what is the int of du??
Original post by asem93
Okay so the integral of u^2 is u^3/3 but what is the int of du??


I don't want to answer that question as it will reinforce your misconception.

The integral of u^2 is meaningless.

The integral of u^2 du is u^3/3.

The du bit isn't just there to look pretty, it is as vital as putting your trousers on when you go to the shops.
Double Angle Formula to define sin^2x in terms if cos2x..

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