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C4 integration please please help

ok here goes, I have a problem that I just can't do, can anyone help me out

∫x2sin(1/2x) dx

but between the boundries 2pi and pi (i don't know how to show that on a comp)

can anyone please help
sara

Reply 1

Knogle

Is that

\Huge\int_\pi^{2\pi} x^2 \sin\left(\frac{1}{2x}\right) dx

Reply 2

sarax

x/2 instead of 1/2x but the rest is right yeah

Reply 3

meef cheese

u = x => du/dx = 1

dv/dx = sin(x/2) => v = -2cos(x/2)

I = uv - u'v
= -2xcos(x/2) + 2 INT cos(x/2) dx
= -2xcos(x/2) + 4 sin(x/2)

and then plug in the limits to get 4pi - 4

Reply 4

sarax

i see your point, but doesn't u need to equal x^2 not x....
and then it doesn't work...????

Reply 5

meef cheese

Ahh, sorry I didn't see that it was x².

Let I denote the integral and integrate by parts twice. [ie. once to get it into terms of cos(x/2), then again to get it back into terms of sin(x/2)]. You'll have I = ... on the left hand side and some fraction of I on the RHS. Bring them over to the same side and that shold give you a solution.

Reply 6

sarax

ok so i just have to do it twice...
if i stick my answer up will ya tell me if its right??
sara

Reply 7

sarax

e-unit

u = x => du/dx = 1

dv/dx = sin(x/2) => v = -2cos(x/2)

I = uv - u'v
= -2xcos(x/2) + 2 INT cos(x/2) dx
= -2xcos(x/2) + 4 sin(x/2)

and then plug in the limits to get 4pi - 4