The Student Room Group
jonnymcc2003
Express as the sum of partial fractions

2/x(x + 1)(x +2)

Hence show that when integrated, between x =4 and x = 2 it equals 3 ln3 - 2 ln5

Cheers.

2=a/(x)+b/(x+1)+c/(x+2)
2=a(x+1)(x+2)+b(x)(x+2)+c(x)(x+1)
x=-1
2=b(-1)(1)
b=-2
x=-2
2=c(-2)(-1)
c=1
x=0
2=a2
a=1
so 2=1/(x+2)-2/(x+1)+1/(x)
intergrating
=[ln(x+2)-2ln(x+1)+lnx] between x=4 and 2
[ln(4+2)-2ln(4+1)+ln4]-[ln(2+2)-2ln(2+2)+ln2]
ln6-2ln5+ln4-ln4+2ln4-ln2
ln6+2ln4-ln2-2ln5
ln48-2ln5
erm not sure where i went wrong wait a sec
jonnymcc2003
Express as the sum of partial fractions

2/x(x + 1)(x +2)

Hence show that when integrated, between x =4 and x = 2 it equals 3 ln3 - 2 ln5

Cheers.


2 = A (x+1) (x+2) + B x (x+2) + C x ( x+1)

if x = 0
A =1

if x =-1

B= -2

if x = -2

C = 1


so u get 1/x -2/ (x+1) +1/ ( x+2)

integrate it

lnx -2ln(x+1) + ln (x+2)


ln4-2ln5+ln6-ln2+2ln3-ln4

-2ln5+ln6-ln2+2ln3

3ln3 - 2ln5

lol it took me ages!
Reply 3
wots the answer? i got 3ln3 - 2ln 5
wonkey
wots the answer? i got 3ln3 - 2ln 5


how did u gt it
Reply 5
jonnymcc2003
Express as the sum of partial fractions

2/x(x + 1)(x +2)

Hence show that when integrated, between x =4 and x = 2 it equals 3 ln3 - 2 ln5

Cheers.


Partial fraction form:

1/x-2/(x+1)+1/(x+2)

The integral is:

[lnx-2ln(x+1)+ln(x+2)] between 4 and 2 therefore:

[ln4-2ln5+ln6] - [ln2-2ln3+ln4]

=ln1r2r25
Reply 6
tammypotato
how did u gt it

In ur answer, simplify....
ln6 - ln 2 = ln (6/2) = ln 3

And also ur last line should have -2ln5, not +2ln5
Reply 7
tammypotato
how did u gt it


u've done the right thing, u just haven't simplified it from ' ln6 - ln2 -2ln5 + 2ln3......

ln 6 - ln 2 becomes ln (6/2) = ln 3

so ln3 + 2ln3 - 2ln5 = 3ln3 - 2ln5
wonkey
u've done the right thing, u just haven't simplified it from ' ln6 - ln2 -2ln5 + 2ln3......

ln 6 - ln 2 becomes ln (6/2) = ln 3

so ln3 + 2ln3 - 2ln5 = 3ln3 - 2ln5


yeah lol just edit it :tongue: im stoopid sumtimes!
Reply 9
Bhaal85
Partial fraction form:

1/x-2/(x+1)+1/(x+2)

The integral is:

[lnx-2ln(x+1)+ln(x+2)] between 4 and 2 therefore:

[ln4-2ln5+ln6] - [ln2-2ln3+ln4]

=ln1r2r25


This is correct because the answer is:

3 ln3 - 2 ln5 which is ln27 - ln25 which is ln(27/25).
Bhaal85
This is correct because the answer is:

3 ln3 - 2 ln5 which is ln27 - ln25 which is ln(27/25).


u clever boy :biggrin: