Using integration by substitution.
find the exact value of
integral from [0,9/16]
sqrt(1 - sqrt(x))/(sqrt(x))
Do a u substitution.
u= 1- sqrt(x)
du = -(1/(2*sqrt(x)))dx
Change your limits by plugging them into the u equation.
u= 1 - sqrt(0) = 1-0 = 1
u= 1 - sqrt(9/16) = 1-(3/4) = 1/4
Substitute the u values in for x.
The new integral is -2*sqrt(u) du from [1,1/4]
OR
2*sqrt(u) du from [1/4,1]
You integrate and get 2*(2/3)*u^(3/2) evaluated from [1/4,1]. Plug in 1, then plug in (1/4). Subtract these two values and you should get your answer.
I got 7/6 or 1.166667