How do I solve this definite integral problem?

In summary, The conversation involved a person struggling with a problem involving integrating the function 1 + 1/x + x dx over the interval [8,2]. They received help from someone who suggested separating the problem into three smaller ones and using the rule \int \frac{dx}{x} = \ln{|x|}. The person thanked the helper for their assistance.
  • #1
chemical
14
0
ive been trying to do this problem and its annoying!


The function to be integrated: 1 + 1/x + x dx


Interval: [8,2]

when anti differentiating the fuction i get x + x^2/2 + lnx but i don't think the integral of 1/x is lnx...help would be appreciated
 
Last edited:
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  • #2
1
The function to be integrated: 1 + - + x dx
x

What does this mean? + - +?

cookiemonster
 
  • #3
sorry updated on error
 
  • #4
You can separate the problem into three little ones.

[tex]\int_2^8 \left( 1 + \frac{1}{x} + x \right) \,dx = \int_2^8 1 \, dx + \int_2^8 \frac{1}{x} \, dx + \int_2^8 x \, dx [/tex]

And

[tex]\int \frac{dx}{x} = \ln{|x|}[/tex]

cookiemonster
 
  • #5
thanks a lot cookie. kudos goes out to you :smile:
 

1. What is a definite integral problem?

A definite integral problem is a mathematical problem that involves finding the exact area under a curve between two specified boundaries. It is a fundamental concept in integral calculus and is used to solve a variety of real-world problems.

2. How is a definite integral problem solved?

A definite integral problem is solved by using the fundamental theorem of calculus, which states that the definite integral of a function can be calculated by finding the antiderivative of the function and evaluating it at the boundaries of the integral.

3. What are the applications of definite integrals?

Definite integrals have many applications in various fields, such as physics, engineering, economics, and statistics. They can be used to calculate areas, volumes, work, and other physical quantities.

4. What is the difference between a definite integral and an indefinite integral?

The main difference between a definite integral and an indefinite integral is that a definite integral has specific boundaries while an indefinite integral does not. A definite integral gives a numerical value, while an indefinite integral gives a general equation.

5. How can I check if my solution to a definite integral problem is correct?

You can check your solution to a definite integral problem by using the properties of integrals, such as the linearity property, the power rule, and the substitution rule. Additionally, you can use software or online calculators to verify your answer.

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