Expert: Ahmed Salami - 2/7/2006

Question
integrate 1/xrootx dx from 0 to 3

Answer
Hi Tara,
Sorry for the time it took.
We start by simplifying 1/x(sqrtx) using the laws of
indices.
sqrtx = x^(1/2)
Using (x^a).(x^b) = x^(a+b)
x(sqrtx) = (x^1).[x^(1/2)] = x^(3/2)
Another of the law states that
1/(x^n) = x^(-n)
And so,
1/x(sqrtx) = 1/x^(3/2) = x^(-3/2)
Remembering that the integral of x^n = x^(n+1) / n+1
We conclude that the integral of 1/x(sqrtx) with
respect to x becomes
$x^(-3/2) dx    ($ represents the integral sign)
= x^(-3/2 + 1) / -3/2 + 1  + c  (c is constant)
= x^(-1/2) / -1/2  + c
= -2x^(-1/2) + c
which could then be simplified to -2/x^(1/2) i.e
-2/sqrtx + c
I hope i have helped. You can always get back to me.
Regards.