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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?

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Answer:

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

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