How do you integrate #int xsqrt(x^2+4)# by trigonometric substitution?
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To integrate ( \int x \sqrt{x^2 + 4} ) by trigonometric substitution, you can use the substitution ( x = 2\tan(\theta) ). Here are the steps:
- Substitute ( x = 2\tan(\theta) ).
- Calculate ( dx ) in terms of ( d\theta ).
- Substitute the expressions for ( x ) and ( dx ) into the integral.
- Simplify the integral in terms of ( \theta ).
- Integrate with respect to ( \theta ).
- Finally, substitute back ( \theta ) in terms of ( x ) to get the answer.
Following these steps, you should be able to integrate ( \int x \sqrt{x^2 + 4} ) using trigonometric substitution.
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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.
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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