Question

Evaluate each of the following integrals, using a trigonometric substitution. Do not forget the back substitution. Solving using other methods is not acceptable.

a. ᶴ dx/√x²+9
b. ᶴ1/x²√16-x² dx
c. ᶴ x/√x²-4 dx

Answer 1

To evaluate each of the given integrals using a trigonometric substitution, we can use the following substitutions: x = 3tan(θ), x = 4sin(θ), and x = 2sec(θ). After simplifying and performing the integration, we need to back-substitute the original variable in each case to find the final answer.

Step-by-step explanation:

To evaluate each of the given integrals using a trigonometric substitution, we can use the following substitutions:

1. For ∫ dx/√(x²+9), substitute x = 3tan(θ).
2. For ∫ 1/x²√(16-x²) dx, substitute x = 4sin(θ).
3. For ∫ x/√(x²-4) dx, substitute x = 2sec(θ).

After simplifying and performing the integration, we need to back-substitute the original variable in each case to find the final answer.

To evaluate each of the given integrals using a trigonometric substitution, we can use the following substitutions: x = 3tan(θ), x = 4sin(θ), and x = 2sec(θ). After simplifying and performing the integration, we need to back-substitute the original variable in each case to find the final answer.