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

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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

How do you evaluate the integral int 1/(4-x)^(3/2)dxint 1/(4-x)^(3/2)dx from 00 to 44?