# Simple integration but i cant get the answer

• semc
In summary, when integrating from 0 to infinity, an improper integral, you must use limits to evaluate it and do not substitute infinity.
semc
$$\int xe^-^x^/^3dx$$ Integrating from 0 to infinity.

So i did this by parts and end up with -3( $$\frac{x}{e^x^/^3}$$ + $$\frac{3}{e^x^/^3}$$ ) x is from 0 to infinity. So for $$\frac{x}{e^x^/^3}$$ if we sub in infinity it would be infinity/infinity? How do we do that?

I am not really sure if it applies here but remember with horizontal asymptotes, if we were to have for example 3x/x, as x goes to infinity, it is a horizontal asymptote at 3 right?

semc said:
$$\int xe^-^x^/^3dx$$ Integrating from 0 to infinity.

So i did this by parts and end up with -3( $$\frac{x}{e^x^/^3}$$ + $$\frac{3}{e^x^/^3}$$ ) x is from 0 to infinity. So for $$\frac{x}{e^x^/^3}$$ if we sub in infinity it would be infinity/infinity? How do we do that?

No, you don't substitute infinity - ever. Because infinity is one of the limits of integration, this is what is called an improper integral, so you need to use limits to evaluate it.
$$\int_0^{\infty} xe^{-x/3}dx~=~\lim_{b \to \infty}\int_0^b xe^{-x/3}dx$$

Since you already have found the antiderivative, evaluate it at b and at 0, and take the limit as x approaches infinity. You will probably need to use L'Hopital's Rule for the x/e^(x/3) term.

## 1. What is integration?

Integration is a mathematical concept that involves finding the value of a function between two given points. It is often used to calculate the area under a curve or the volume of a three-dimensional shape.

## 2. How do you perform integration?

The process of integration involves finding an antiderivative of a given function and then evaluating it at the bounds of the integration. This can be done using various methods such as substitution, integration by parts, or using tables of integrals.

## 3. What is simple integration?

Simple integration refers to integration problems that can be solved using basic integration techniques, such as those mentioned above. These problems usually involve simple functions and have well-defined bounds of integration.

## 4. Why can't I get the answer for a simple integration problem?

There could be various reasons for not being able to get the answer for a simple integration problem. Some possible reasons include making an error in the integration process, not having enough information or incorrect information about the bounds of integration, or using an incorrect method for solving the problem.

## 5. How can I improve my integration skills?

Practicing integration problems regularly and understanding the concepts behind different integration techniques can help improve your integration skills. You can also seek help from a teacher or tutor if you are having trouble understanding a specific concept or solving a problem.

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