Illustrate an integral expression?

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SUMMARY

The discussion centers on the integral expression for the function f(x) = ln(√(4x - 16)) evaluated at f(5). The key point is that the natural logarithm, ln(x), can be expressed as an integral: ln(x) = ∫(1 to x) (1/t) dt. Participants express confusion about the term "illustrate an integral expression" and the necessity of writing it out, particularly when direct evaluation seems simpler. The correct approach involves defining the function and applying the integral definition of the natural logarithm.

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  • Understanding of natural logarithms and their properties
  • Familiarity with integral calculus concepts
  • Knowledge of function evaluation techniques
  • Basic skills in mathematical notation and expressions
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  • Study the properties of natural logarithms, specifically ln(x) = ∫(1 to x) (1/t) dt
  • Explore integral calculus techniques for evaluating definite integrals
  • Learn how to manipulate and simplify expressions involving square roots
  • Practice writing and illustrating integral expressions for various functions
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Students in calculus, mathematics educators, and anyone seeking to deepen their understanding of integral expressions and logarithmic functions.

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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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[tex]\ln x =\int_{1}^{x} \frac{dt}{t}[/tex] just to get you started.
 

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