calculus II
posted by Alex .
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) = 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
Respond to this Question
Similar Questions

Calculus URGENT test tonight
Integral of: __1__ (sqrt(x)+1)^2 dx The answer is: 2ln abs(1+sqrt(x)) + 2(1+sqrt(X))^1 +c I have no clue why that is! Please help. I used substitution and made u= sqrt(x)+1 but i don't know what happened along the way! Your first … 
Math Help please!!
Could someone show me how to solve these problems step by step.... I am confused on how to fully break this down to simpliest terms sqrt 3 * sqrt 15= sqrt 6 * sqrt 8 = sqrt 20 * sqrt 5 = since both terms are sqrt , you can combine … 
Calculus
so we are doing integrals and I have this question on my assignment and I can't seem to get it, because we have the trig substituion rules, but the number isn't even so its not a perfect square and I just cant get it, so any help would … 
Calculus
Graph the curve and find its exact length. x = e^t + e^t, y = 5  2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t  e^t, correct? 
Calculus
Please look at my work below: Solve the initialvalue problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/ Sqrt(4^24(1)(6)))/2(1) r=(16 +/ Sqrt(8)) r=8 +/ Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 … 
Math/Calculus
Solve the initialvalue problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else? 
Calculus
Find the volume of the solid whose base is the region in the xyplane bounded by the given curves and whose crosssections perpendicular to the xaxis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, … 
Calculus
Evaluate the indefinite integral: 8xx^2. I got this but I the homework system says its wrong:sqrt((x8)x)/(2*sqrt(x8)*sqrt(x))*(((sqrt(x8)*(x4)*sqrt(x))32*log(sqrt(x8)+sqrt(x)) 
Calculus
Hi. In an integration solution, the integral of (1/(sqrt (8u squared)) is written as arcsin(u/sqrt 8), but I don't see how they got it. When I did it I got (1/8)*(arcsin(u*sqrt8)). What I did was take sqrt8 common in the denominator … 
Calculus 2 (Differential Equation)
How would you solve the following problem explicitly?