# How do you integrate #int sqrt(9-x^2)# using trig substitutions?

From double angle formula

Apply double angle formula:

By signing up, you agree to our Terms of Service and Privacy Policy

By signing up, you agree to our Terms of Service and Privacy Policy

To integrate ( \int \sqrt{9-x^2} ) using trigonometric substitution, you can let ( x = 3\sin(\theta) ), then ( dx = 3\cos(\theta)d\theta ). Substitute these into the integral, simplify, and then use trigonometric identities to evaluate it. This will lead you to the integral of ( \cos^2(\theta) ), which can be further simplified using trigonometric identities. Finally, integrate and back-substitute ( \theta ) in terms of ( x ) to find the result.

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7