NationStates Jolt Archive

integral of e^s(sin(t-s))ds from t to 0

i kno whow to use the integration by parts rule but something needs to be done to make the t into an s

Integration is against my religion, so I can't help you. If it was differentiation, I'd totally help you though...

**goes out on a limb**

Isn't the t a constant? and therefore doesn't need to be changed into an s

|Edit: That was my three thousandth post!?! FFS:(

**goes out on a limb**

Isn't the t a constant? and therefore doesn't need to be changed into an s

|Edit: That was my three thousandth post!?! FFS:(

spanks

:fluffle:

i feel special

Isn't the t a constant? and therefore doesn't need to be changed into an s

HMW is correct. For the purposes of the integration, t is a constant.

HMW is correct. For the purposes of the integration, t is a constant.

Booyah!

so then u=e^s
du=(e^s)ds
dv= sin(t-s)ds
v=cos(t-s)

are those right for integration by parts method?

end result:

(e^s)(cos(t-s))-(e^S)(sin(t-s))

i think i did something wrong

:headbang:

so then u=e^s
du=(e^s)ds
dv= sin(t-s)ds
v=cos(t-s)

are those right for integration by parts method?

I'm confused by the original question. Is it

(e^s)(sin{t-s})ds

or

e^(s(sin{t-s}))

?

If it's the first one, then yes, I believe you are correct.

If it's the second (which I doubt, but then I have no idea how old you are or even how the American education system paces this stuff) then you would be wrong.

I'm confused by the original question. Is it

(e^s)(sin{t-s})ds

or

e^(s(sin{t-s}))

?

If it's the first one, then yes, I believe you are correct.

If it's the second (which I doubt, but then I have no idea how old you are or even how the American education system paces this stuff) then you would be wrong.


its the first one, and im not sure if the end result is right

thanks for your help by the way

thanks for your help by the way

No problem.:)

To find out if your end result is right, differentiate it. If you get e^s sin(t-s) after differentiating, you did it right (or differentiated incorrectly).

end result:

(e^s)(cos(t-s))-(e^S)(sin(t-s))

i think i did something wrong

:headbang:

If you let y=e^s(sin(t-s))ds

then you have y=(e^s)(cos(t-s))-y

2y=(e^s)(cos(t-s))

y=((e^s)(cos(t-s))/2)

then slap the limits in and it should work

e^s sin(t-s) ds
u = e^s
du = e^s ds
dv = sin(t-s) ds
v = cos(t-s)

∫e^s sin(t-s) ds = e^s cos(t-s) - ∫e^s cos(t-s) ds

u = e^s
du = e^s ds
dv = cos(t-s) ds
v = - sin(t-s)

∫e^s sin(t-s) ds = e^s cos(t-s) + e^s sin(t-s) - ∫e^s sin(t-s) ds
2∫e^s sin(t-s) ds = e^s cos(t-s) + e^s sin(t-s)

∫e^s sin(t-s) ds = e^s (cos(t-s) + sin(t-s))/2

Then plug in 0 and t.