Question

If the change of variables uequalsx2plus1 is used to evaluate the definite integral Integral from 5 to 9 f (x )dx​, what are the new limits of​ integration?

Answer 1

The new lower limit of integration is 26 and the new upper limit of integration is 82.

Explanation:

If the substitution for the definite integral from 5 to 9 is given by:

`u=x^2+1`

Then the new limits of integration are:

New lower limit:

Evaluate 5 in u:

`u=(5)^2+1=25+1=26`

New upper limit.

Evaluate 9 in u:

`u=(9)^2+1=81+1=82`