Very Urgent P5 Reduction Formula Watch

This discussion is closed.
zxcvbnm
Badges: 0
#1
Report Thread starter 14 years ago
#1
can any one please help me with the following , its very urgent and its on the specification so might come up in the exam

I(n) = int ((sin nx)/(sin x)) n>0

show that ,

I(n+2) = [ 2sin (n+1)x ] + I(n)
-------------
( n+1 )

i need urgent help ..plz can any one do this or give an hint ...plz...
0
zxcvbnm
Badges: 0
#2
Report Thread starter 14 years ago
#2
sorry (n+1) is the denominator of [2sin (n+1)x ]
0
Giraffeboy
Badges: 0
#3
Report 14 years ago
#3
OK, I thought I was sorted on P5, thanks for pointing this out to me. ARGGGHH - OK, plan B, hope this doesn't come up
0
zxcvbnm
Badges: 0
#4
Report Thread starter 14 years ago
#4
its also question 12 exercise 3D page 55 the heninmann book P5

plz some one should be able to do it..
0
zxcvbnm
Badges: 0
#5
Report Thread starter 14 years ago
#5
yeah i was confident but when i checked specs i got scared
0
qqqwwweee
Badges: 2
Rep:
?
#6
Report 14 years ago
#6
In+2
= INT [sin(n+1)xcosx + sinxcos(n+1)x]/sinx dx
= INT sin(n+1)x cosx / sinx dx + INT cos(n+1)x dx
= INT sin(n+1)x / sinx d(sinx) + 1/(n+1) sin(n+1)x (then use by parts to deal with the first one)
= sin(n+1)x - INT sinx [(n+1)sinx cos(n+1)x - sin(n+1)x cosx ]/ sin^2x dx + + 1/(n+1) sin(n+1)x
= (n+2)/(n+1) sin(n+1)x - INT [(n+1)sinx cos(n+1)x - sin(n+1)x cosx]/sinx dx
= (n+2)/(n+1) sin(n+1)x - INT [nsinx cos(n+1)x + sin(-nx)]/sinx dx
= (n+2)/(n+1) sin(n+1)x - INT ncos(n+1)x dx + INT sin(nx)/sinx dx
= (n+2)/(n+1) sin(n+1)x - n/(n+1)sin(n+1)x + In
= 2/(n+1) sin(n+1)x + In

Actually it is one of the most difficult integrals I ve ever seen!
0
X
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of the Arts London
    MA Design: Ceramics, Furniture or Jewellery Open Day Postgraduate
    Fri, 25 Jan '19
  • Coventry University
    Undergraduate Open Day Undergraduate
    Sat, 26 Jan '19
  • Brunel University London
    Undergraduate Experience Days Undergraduate
    Sat, 26 Jan '19

Are you chained to your phone?

Yes (109)
19.82%
Yes, but I'm trying to cut back (223)
40.55%
Nope, not that interesting (218)
39.64%

Watched Threads

View All