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) = 10 = 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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