U-substitution question

Question

How do you know when to change the limits of integration when doing u-substitution?

Would it be wrong to use the limits given?

Answer 1

Hi Affar,

The limits of integration do need to be changed during u-substitution if you plan on solving the whole integration, including plugging in the limits, keeping the problem in terms of u.

If you solve the integral and switch all of your variables back to x before plugging the limits in for the final solution, then you will not need to change your limits.

The limits for both x and u are actually describing the same limit, just in terms of 2 different variables. They are related to each other in the same way that x and u are related to each other!

Hope this helps! Let me know if you have any more questions on this! :)

-Davis

Answer 2

The integration limits are associated with a specific variable. If you substitute variables, you have to either change the limits by making an equivalent substitution, or you have to wait to back substitute to the original variable before evaluating. Usually, changing the limits wil result in an easier evaluation since the expression should be simpler.