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# P5 questions help, thread:) watch

1. x = cosθ
dx = - sinθ dθ

I(n) = - pi/20 cosnθ . sinθ . sinθ dθ
= - pi/20 cosn sin²θ dθ
= 0pi/2 cosn sin²θ dθ

You want I(5).
2. Very sorry guys. I made a typo in the question. It's:

In = ∫ xn.√(1-x)

Heh. The reason I typed (1-x^2), was because I tried the cosθ substitution, and frustratingly got the (1-x^2) rather than (1-x). Must've confused me or something.
3. (Original post by Lucky Penny)
god how did you do the first part??
I would expect it was integration by parts. Differentiate and integrate
4. (Original post by mockel)
Very sorry Gaz. I made a typo in the question. It's:

In = ∫ xn.√(1-x)
Then you're going to have to use x=cos²θ with dx=-2sinθcosθ, I think.
5. Cool, I'll give it a go...
6. In the P5 exam, are we expected to know the t substitution and....for example what dt/dx is in this case...?
7. (Original post by lgs98jonee)
In the P5 exam, are we expected to know the t substitution and....for example what dt/dx is in this case...?
t = tan(x/2)?
Well you can always derive dt/dx (very quick), along with the sin and cos ones (these are given, but also quick to derive)

Oh, and the reduction one looks good now. Cheers.
8. btw dont know if u noticed but the t=tan(x/2) is in F/B on page6 at top
10. lol see other post! and stick to 1 post only dont spam
11. Which part do you need help with?
12. I am surprised about not being able to do this for sure.#

differentiate y=x^sinhx

is it dy/dx=coshx.sinhx.a^sinhx

:/
13. hey i got stuck on either question 3 or 4 in the exam paper at the end of the book, its the one that involves y=mx+c... runs to room to get book
14. If that's from the sample exam at the end of the P5 book, then it should be y=x^x, not x^sinhx.
15. er which other post would that be syncman??

the first part dvs..
16. hahahaha its impossible i spent hours trying it! back of P5 book.. should be y= x^x
17. (Original post by lgs98jonee)
I am surprised about not being able to do this for sure.#

differentiate y=x^sinhx

is it dy/dx=coshx.sinhx.a^sinhx

:/
Is this from the exam style paper at the back of the P5 book? If so there's an error where should read .
If not:
18. (Original post by Lucky Penny)
er which other post would that be syncman??

the first part dvs..
http://www.thestudentroom.co.uk/show...97&postcount=9
19. (Original post by Lucky Penny)
er which other post would that be syncman??

the first part dvs..
xy = c²
y + x(dy/dx) = 0
dy/dx = -y/x

So at P, dy/dx = -(c/t)/ct = -1/t². And hence the gradient of the normal is t², and it's equation is:
y - c/t = t²(x - ct)
y = t²x + c/t - ct³
20. (Original post by Lucky Penny)
8. a)
P(ct,c/t)

y=ct-1
dy/dt = -ct-2

x=ct
dx/dt = c

dy/dx = dy/dt . dt/dx
=-c/(ct²)
hence normal = t²

t - y1 = m(x-x1)
y-c/t=t²(x-ct)
y=t²x-ct3+c/t

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