How do you evaluate the integral #int 1/(4-x)^(3/2)dx# from #0# to #4#?

Question

4633 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-03T12:53:12

This integral does not converge

we can try #t = 4-x implies dt = - dx#

the integration becomes

# - int_(4)^(0) \ t^(-3/2) \ dt#

#= int_(0)^(4) \ t^(-3/2) \ dt#

#= [ \ -2 t^(-1/2) ]_(0)^(4)#

#= [ \ -2/sqrt t ]_(0)^(4)#

Ouch! We can look at this....

#= lim_{p to o} [ \ -2/sqrt t ]_(p)^(4) to oo#

This integral does not converge