How Do You Calculate the Area Under the Curve f(x) = 9/x from 5 to 10?

In summary, the function F(x) is given as 9/x and we are asked to find the area under its graph on the interval [5, 10]. It is unclear if F(x) and f(x) are the same function, and if F(x) is the anti-derivative of f(x). To find the area, we can evaluate the anti-derivative of F(x) from 5 to 10, which is 9ln|x| + c.
  • #1
mathdum
2
0
Find the area of the region under the graph of the function f on the interval [5, 10].
F(x) = 9/x
 
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  • #2
When you say that F(x) = 9/x, do you mean that F'(x) = f(x) where f(x) is the function whose area under its curve you want to calculate? Or did you mistakenly capitalize "f"?
 
  • #3
Well, my problem just says F(x). Other problems have F'(x), However, this one does not. Hmm...
 
  • #4
mathdum said:
Well, my problem just says F(x). Other problems have F'(x), However, this one does not. Hmm...

Usually capitalized notation means that it is the anti-derivative. This means you should evaluate F from the given bounds. Do you know how to do this?
 
  • #5
mathdum said:
Find the area of the region under the graph of the function f on the interval [5, 10].
F(x) = 9/x
Try to be precise in the relationship between F(x) and f(x).
 
  • #6
9ln|x| + c
 

FAQ: How Do You Calculate the Area Under the Curve f(x) = 9/x from 5 to 10?

1.

What is the definition of an anti derivative of a fraction?

An anti derivative of a fraction is a function that, when differentiated, results in the given fraction.

2.

How do you find the anti derivative of a fraction?

To find the anti derivative of a fraction, you must use the power rule, chain rule, and/or product rule in reverse. You can also use known anti derivative formulas for common fractions.

3.

What is the difference between an anti derivative and an indefinite integral?

While both refer to the reverse process of differentiation, an anti derivative is a specific function that, when differentiated, results in the given fraction. An indefinite integral, on the other hand, represents a family of functions that differ by a constant.

4.

Are there any specific rules for finding the anti derivative of a fraction?

Yes, there are specific rules and formulas for finding the anti derivative of common fractions such as polynomials, trigonometric functions, and exponential functions. These rules include the power rule, chain rule, and product rule.

5.

What is the importance of knowing how to find the anti derivative of a fraction?

Knowing how to find the anti derivative of a fraction is important in many areas of mathematics and science, particularly in calculus. It allows us to solve problems involving rates of change, optimization, and area under a curve. It also helps us understand the relationship between a function and its derivative.

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