Illustrate an integral expression?

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Homework Statement



let f(x) = ln of the square root of (4x-16)

using the definition of ln x, write and illustrate an integral expression for f(5)

Homework Equations



n/a

The Attempt at a Solution



im confused on even what its asking. what does it mean to illustrate an integral expression? does it mean to write it out with the integral symbol? and why write an integral expression when the question doesn't even ask for it?

and what is the definition of ln x? i didnt even know it had a definition. i just know it means log base e (ie, e^y = x)

and for f(5), why can't i simply plug it in and get ln of the square root of 4 = ln 2?

can someone clarify what this question is asking and how to proceed? thanks and i appreciate any help.
 
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\ln x =\int_{1}^{x} \frac{dt}{t} just to get you started.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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