if the change of variables $u = x^{2}+5$ is used to evaluate the definite integral $int_{5}^{9}f(x) dx$…
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?
Answer
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.