Posted by **Alex** on Saturday, December 10, 2011 at 5:26pm.

Using integration by substitution.

find the exact value of

integral from [0,9/16]

sqrt(1 - sqrt(x))/(sqrt(x))

- calculus II -
**Katie**, Saturday, December 10, 2011 at 6:23pm
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

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