Chapter 7.4, Problem 57E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

1. a. If x = 4 tan θ, then csc θ = 4/x.
2. b. The integral ${\displaystyle {\int }_1^2\sqrt{1-x^2}dx}$ does not have a finite real value.
3. c. The integral ${\displaystyle {\int }_1^2\sqrt{x^2-1}dx}$ does not have a finite real value.
4. d. The integral ${\displaystyle \int \frac{dx}{x^2+4x+9}}$ cannot be evaluated using trigonometric substitution.