Question

if the change of variables $u = x^{2}+5$ is used to evaluate the definite integral $int_{5}^{9}f(x) dx$, what are the new limits of integration?

Explanation:

Step1: Find the lower - new limit

When \(x = 5\), substitute into \(u=x^{2}+5\).
\(u_1=5^{2}+5=25 + 5=30\)

Step2: Find the upper - new limit

When \(x = 9\), substitute into \(u=x^{2}+5\).
\(u_2=9^{2}+5=81 + 5=86\)

Answer:

The lower limit is 30 and the upper limit is 86.