Find minimum value of a to get minimum area

[winter]

Integrate a function change limits

Do you always change the limits of integration when using u du patterns ? How do you know when to change the limits of integration?

 

[SAMUELK]

Do you always change the limits of integration when using u du patterns ? How do you know when to change the limits of integration?

(This post seems misplaced.)

I prefer the term 'boundary' to 'limit' here, BUT:

If you change the variable, commonly called a 'u-substitution', then yes, you are always required to change them. HOWEVER, If:

1) You will change back to x at the end, [which you do MOST of the time, but not always]

and

2) Your teacher isn't looking,

you don't have to.

Naturally there are situations where you won't change back, and then you certainly must change the boundary points. It's good practice to. It's also good practice for you, too.