u substitution (1 Viewer)

[turnerloos]

when you integrate using u sub and say you let u^2 = x + 1. When you find the limits for the integral, would "u" be plus, minus? why, why not?

 

[Trebla]

Ideally you should be defining 'u' as a function which has a unique inverse to avoid this problem. In this case define it more specifically as either the positive or negative square root. In either case, the solution would be the same though.

 

[Carrotsticks]

when you integrate using u sub and say you let u^2 = x + 1. When you find the limits for the integral, would "u" be plus, minus? why, why not?

The substitution has to be one-to-one to avoid this problem. Your substitution, as it currently is, is not one-to-one.

So to resolve it, it should more accurately be u^2=x+1, where u>0 or u<0.

Now, you can go ahead and choose your limits according to whether you assigned u>0 or u<0.