# definite integration

• Sep 3rd 2007, 03:51 PM
xfyz
definite integration
The integral of [ 1 / t^3 * sqrt(t^2 - 1) ] from sqrt(2) to 2.
Can someone help me in getting the integral..

I tried u substitution but got stuck..

u = sqrt(t^2-1)
du/dt = (1/2)(sqrt(t^2-1)^-(1/2)
du = " " * dt

dV = t^3
v = t^4/4

Is this the right way? I get stuck after I rewrite it..

is there an easier way, thank you
• Sep 3rd 2007, 03:56 PM
Jhevon
Quote:

Originally Posted by xfyz
The integral of [ 1 / t^3 * sqrt(t^2 - 1) ] from sqrt(2) to 2.
Can someone help me in getting the integral..

I tried u substitution but got stuck..

u = sqrt(t^2-1)
du/dt = (1/2)(sqrt(t^2-1)^-(1/2)
du = " " * dt

dV = t^3
v = t^4/4

Is this the right way? I get stuck after I rewrite it..

is there an easier way, thank you

how about trig substitution? $t = \sec \theta$

that's what i immediately thought of when i saw it. i'll try it the integration by parts way to see if i have any luck with it
• Sep 3rd 2007, 04:13 PM
xfyz
Quote:

Originally Posted by Jhevon
how about trig substitution? $t = \sec \theta$

that's what i immediately thought of when i saw it. i'll try it the integration by parts way to see if i have any luck with it

sorry could you explain where you're getting t= sec(-)? Is this an identity or something?
• Sep 3rd 2007, 04:16 PM
Jhevon
Quote:

Originally Posted by xfyz
sorry could you explain where you're getting t= sec(-)? Is this an identity or something?

yes, it's from one of the formulas for "trigonometric substitution." it's in your text, you can look it up