Why hello improper integral, how are you?

In summary, the conversation discusses the solution to the integral from -1 to 1 of 3/x^2 dx, with the attempt at a solution using limits and the discussion of a possible error resulting in an answer of infinity.
  • #1
yeahyeah<3
27
0

Homework Statement


integral from -1 to 1 of 3/x^2 dx


Homework Equations





The Attempt at a Solution


Limit
t --> infinity integral from -1 to t of 3/x^2 dx + limit t --> infinity integral from t to 1 of 3/x^2 dx

Limit
t-> infinity -3/t - (-3/-1) + Limit t--> inifinty (-3/1) - (3/t)

-3 -3 = -6

Now when I check the answer in my calc I get infinity. Thus my answer is probably wrong. Where did I go wrong?
Thanks so much =]
 
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  • #2
Why infinity? It is (a) outside the domain, and (b) you are integrating across the singularity.
 
  • #3
yeahyeah<3 said:
Now when I check the answer in my calc I get infinity. Thus my answer is probably wrong. Where did I go wrong?

Limit
t --> infinity integral from -1 to t of 3/x^2 dx + limit t --> infinity integral from t to 1 of 3/x^2 dx

This should be as t→0.
 

1. What is an improper integral?

An improper integral is an integral that does not have both limits of integration that are finite. This means that either the upper or lower limit of integration is infinite, or that the integrand is undefined at one or more points within the interval of integration.

2. Why are improper integrals important?

Improper integrals are important because they allow us to extend the concept of integration to functions that would otherwise be impossible to integrate. They also have many important applications in physics, engineering, and other scientific fields.

3. How do you evaluate an improper integral?

To evaluate an improper integral, you must first determine whether it is convergent or divergent. If it is convergent, you can use various techniques such as substitution, integration by parts, or partial fractions to evaluate the integral. If it is divergent, the integral does not have a finite value.

4. Can improper integrals have a finite value?

Yes, improper integrals can have a finite value if they are convergent. This means that the integral can be evaluated and the result will be a real number. However, if the integral is divergent, it does not have a finite value.

5. What are some common examples of improper integrals?

Some common examples of improper integrals include integrals with infinite limits of integration, integrals with discontinuous integrands, and integrals with vertical asymptotes in the interval of integration. These types of integrals often arise in calculus problems involving infinite series, differential equations, and areas under curves.

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