if the change of variables $u = x^{2}+5$ is used to evaluate the definite integral $int_{3}^{9}f(x)dx$, what…
if the change of variables $u = x^{2}+5$ is used to evaluate the definite integral $int_{3}^{9}f(x)dx$, what are the new limits of integration?
Answer
Explanation:
Step1: Find lower - limit value
When (x = 3), substitute into (u=x^{2}+5). [u=(3)^{2}+5=9 + 5=14]
Step2: Find upper - limit value
When (x = 9), substitute into (u=x^{2}+5). [u=(9)^{2}+5=81 + 5=86]
Answer:
The new lower - limit is 14 and the new upper - limit is 86.