Question

Why doesn’t the definite integral${\int }_2^3\sqrt{1-x^2}dx$ make sense? (Hint: Think about domains.)

Short answer

Ans: $\sqrt{1-x^2}$is not defined in $[2,3]$.

Step-by-step solution

Step 1. Given information:

${\int }_2^3\sqrt{1-x^2}dx$

Step 2. Proving: 

The definite integral ${\int }_2^3\sqrt{1-x^2}$ does not make sense because the function has a domain in $[-1,1]$. But the limit of the integral is $[2,3]$ which does not come under the domain of the function. That's why $\sqrt{1-x^2}$ is not defined in $[2,3]$.