Finding new limits of integration problem

In summary, the conversation discusses the process of solving two integrals using substitution. The first integral is transformed using u substitution and the bounds are switched and multiplied by -1. The second integral also uses u substitution, but the bounds are not switched or multiplied by -1. The expert suggests that as long as the substitution and rules are applied correctly, it does not matter if the bounds are switched or multiplied by -1.
  • #1
coolguy1
1
0
In the integral

integral(1,infinity) e^(-sqrt(x)) / sqrt(x)

STEP 1:
I let u = -sqrt(x)
du = -1/(2sqrt(x))

then my lower bound u = -1
then my upper bound u = -infinity

-2 integral(-1,infinity) e^u du

I would then switch the order of the integration bounds and multiply by -1My question is in the next problem integral(0,infinity) x^2/(1+x^3) dx
I let u = 1 + x^3
du = 3x^2 dx
du/3 = x^2 dx

lower bound u = 1
upper bound u = infinity

My question is: Would you multiply by -1 and switch the lower and upper bounds in this problem, or was that just the case in the previous problem?Thanks for your help and sorry I'm new to the commands and not sure how to use them yet.
 
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  • #2
In fact, it doesn't matter as long as you apply the rules correctly.
 

FAQ: Finding new limits of integration problem

What is the purpose of finding new limits of integration in a problem?

The purpose of finding new limits of integration in a problem is to simplify the integration process and make it easier to solve. By changing the limits, the integral can be rewritten in a form that is easier to work with and can lead to a more accurate solution.

When should new limits of integration be used in a problem?

New limits of integration should be used when the original limits are difficult to work with or when they do not lead to a solution. By changing the limits, the integral may become solvable or may be easier to solve using other methods.

How do you find new limits of integration?

To find new limits of integration, you can use a change of variables or a substitution. This involves replacing the original variable in the integral with a new variable and then solving for the new limits using the relationship between the new and original variables.

Can new limits of integration change the value of the integral?

Yes, new limits of integration can change the value of the integral. This is because the new limits may result in a different area under the curve or a different value for the function being integrated. It is important to check the accuracy of the solution when using new limits of integration.

Are there any limitations to using new limits of integration?

Yes, there are limitations to using new limits of integration. In some cases, it may not be possible to find new limits that lead to a solution or the new limits may result in a more complex integral. It is also important to consider the validity of the new limits and ensure they accurately represent the original problem.

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