| Account limit of 2000 requests per hour exceeded. |
How would you apply the Beta Function to this integral?
How would the beta function be applied to this integral?
The integral is between 1 and infinity of (t^2 - 1)^(-2/3) dt
u = t^2-1
du = 2t dt ==> dt = du/ (2(u+1)^(1/2))
1/2 ∫ u^(-2/3)/(u+1)^(1/2) du from 0 to infinity
we know that B(x,y) = ∫ t^(x-1)/(1+t)^(x+y) dt from 0 to infty
so
I= 1/2 ∫ u^(-2/3)/(u+1)^(1/2) du from 0 to infinity
x-1 = -2/3 ==> x=1/3
y+x = 1/2 ==> y=1/6
I = 1/2 B(1/3,1/6)
=1/2 ( Γ(1/3) Γ(1/6))/ Γ(1/2)
=Γ(1/3) Γ(1/6) / (2√π)
 |
 INFINITY IRS DELTA GAMMA BETA SERVO CONTROL WOOFER $900.00 Time Remaining: 2d 11h 52m Buy It Now for only: $900.00 |
 REAL RARE INFINITY IRS SERIES V BETA DELTA GAMMA NEO KAPPA EMIT TWEETER $229.99 Time Remaining: 3d 2h 37m Buy It Now for only: $229.99 |
 REAL RARE INFINITY IRS BETA DELTA GAMMA NEO KAPPA sEMIT TWEETER $229.99 Time Remaining: 3d 2h 41m Buy It Now for only: $229.99 |
 InFiNiTy BeTa ES250 W Speakers BRanD NeW PAIR BLACK in COLOR $299.99 Time Remaining: 5d 9h 14m Buy It Now for only: $349.99 |
 Infinity Beta 50 Tower Speakers PAIR $299.00 Time Remaining: 13d 1h 38m Buy It Now for only: $299.00 |
 INFINITY IRS DELTA GAMMA BETA SERVO CONTROL CABLES $222.22 Time Remaining: 13d 19h 54m Buy It Now for only: $222.22 |
 INFINITY IRS LEMIM MIDRANGE MID for IRS BETA GAMMA DELTA VERY RARE TESTED $1,099.99 Time Remaining: 21d 23h 3m Buy It Now for only: $1,099.99 |
 INFINITY 12 902 3054 WOOFERS for BETA and DELTA GAMMA TESTED PAIR NICE REFOAMED $299.99 Time Remaining: 22d 4h 45m Buy It Now for only: $299.99 |
 INFINITY IRS 30 SERVO CONTROL CABLES for BETA and DELTA GAMMA SERVO NICE PAIR $222.22 Time Remaining: 22d 16h 47m Buy It Now for only: $222.22 |