# How to solve #\intx^2\sqrt(9-x^2)dx# with integration by parts?

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Does it involve trig substitution?

Does it involve trig substitution?

the answer

show the steps

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To solve the integral ∫x^2√(9-x^2) dx using integration by parts, follow these steps:

- Let u = x^2 and dv = √(9 - x^2) dx.
- Compute du and v.
- Apply the integration by parts formula: ∫u dv = uv - ∫v du.
- Substitute the values of u, dv, du, and v into the integration by parts formula.
- Evaluate the resulting integral.
- Simplify the expression to obtain the final answer.

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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.

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