# How do you integrate #int x^2sqrt(16-x^2)# by trigonometric substitution?

The answer is

Perform the substitution

Therefore,

The integral is

Therefore,

And finally,

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

To integrate ( \int x^2\sqrt{16-x^2} ) using trigonometric substitution, perform the following steps:

- Let ( x = 4\sin(\theta) ).
- Then, ( dx = 4\cos(\theta) d\theta ).
- Substitute ( x ) and ( dx ) in the integral.
- Simplify the integrand using trigonometric identities.
- Integrate the simplified expression.
- Finally, substitute back the original variable ( x ) in terms of ( \theta ).

Following these steps, the integral can be solved using trigonometric substitution.

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

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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