Question

Using the trigonometric substitution, the integral

I=∫d x/(x²-25) √(x²-25)
is equal to the integral, in terms of θ,
I=∫ d θ

Answer 1

To evaluate the given integral using trigonometric substitution, we can substitute x = 5 sec θ. After making this substitution, the integral simplifies to ∫5 tan θ d θ, which can be easily integrated.

Step-by-step explanation:

To evaluate the integral ∫d x/(x²-25) √(x²-25) using trigonometric substitution, we can substitute x = 5 sec θ. This substitution is made because it simplifies the integral and allows us to express it in terms of the θ variable. After making the substitution, the integral becomes ∫(5 sec θ)^2 / (5 sec θ)^2 * 5 tan θ sec θ. We simplify this to ∫5 tan θ d θ, which can be easily integrated to give us the final result.