Illustrate an integral expression?

In summary, the task is to use the definition of ln x to write and illustrate an integral expression for f(5), where f(x) = ln√(4x-16). The definition of ln x is equal to the integral of 1/t with limits of 1 and x. This means that the integral expression for f(5) would be equal to ln(√(4x-16)) with the limits of 1 and 5. It cannot simply be plugged in, as the expression is a function and requires the use of the integral symbol.
  • #1
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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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  • #2
[tex] \ln x =\int_{1}^{x} \frac{dt}{t} [/tex] just to get you started.
 

1. What is an integral expression?

An integral expression is a mathematical expression that represents the area under a curve on a graph. It is used to calculate the accumulation of a quantity over a certain interval.

2. How do you illustrate an integral expression?

To illustrate an integral expression, you can use a graphing calculator or plot the function on a graph paper. You can also use a computer program, such as Microsoft Excel, to generate a graph of the integral expression.

3. What is the purpose of an integral expression?

The purpose of an integral expression is to calculate the total value of a quantity over a given interval. It is commonly used in calculus and other areas of mathematics to solve problems involving rates of change and accumulation.

4. What are some common notations used for integral expressions?

Some common notations used for integral expressions include the integral sign (∫), the variable of integration (often x or t), the function being integrated, and the limits of integration. For example, ∫ f(x) dx represents the integral of f(x) with respect to x.

5. How do you evaluate an integral expression?

To evaluate an integral expression, you can use various integration techniques, such as substitution, integration by parts, or partial fractions. You can also use numerical methods, such as the trapezoidal rule or Simpson's rule, to approximate the value of the integral. Additionally, some integrals can be evaluated using tables of integrals or with the help of a graphing calculator.

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