U-substitution

[awibroe]

hello all,

i am trying to get my head around integration by substitution.

in a simple case of the integrand (x-1)/2 dx  I know the answer is (x^2/4)-(x/2).

if I try to do this by substitution, I get a bit lost.

ive gone as follows:

u= x-1

du=1*dx

dx=du

(u/2)du

(u^2)/4

(x-1)^2/4

(x^2-2x+1)/4

obviously this is not correct. Does anyone know what I'm doing wrong?

‌

[AlanStevens · Accepted solution]

You have done it correctly!  The apparent difference is because an indefinite integral is only defined to within an arbitrary constant.  The two forms you show are the same to within an arbitrary constant.

Alan

[awibroe]

‌Alan,

thanks for that, interesting!

so if I make the original integral limited between 2 and 4 I believe the end result ends up being 2. When doing this for the substitution method, the limits I believe become 1 and 3 noting that my I value is x-1. This produces an answer of 1 not 2?

andy

[Fred_Kohlhepp]

Looks like the same answer to me!

[awibroe]

I know what I have done wrong. Yes Fred it is indeed correct.

Fascinating stuff!

Andy