What is the integral of cos t/t where limits are 1 to x ?
My book says that it is sinx/x - sin1 + integral (from 1 to x) sin t/ t2 dt for all x>=1.
I can't figure out how .
Please help.
Printable View
What is the integral of cos t/t where limits are 1 to x ?
My book says that it is sinx/x - sin1 + integral (from 1 to x) sin t/ t2 dt for all x>=1.
I can't figure out how .
Please help.
Quote:
Originally Posted by mrmaaza123
Use integration by parts.
$\displaystyle u=\frac{1}{t} \implies du=-\frac{1}{t^2}dt$
and
$\displaystyle dv=\cos(t) \implies v=\sin(t)$
This gives
$\displaystyle \int_{1}^{x} \frac{\cos(t)}{t}dt=\frac{\sin(t)}{t}\bigg|_{t=1}^ {t=x}+\int_{1}^x\frac{\sin(t)}{t^2}dt$
Oh, yes. Thank you, i don't really know how i overlooked that !
