How do you integrate #int 1/sqrt(x^2-4x-21)dx# using trigonometric substitution?
Christopher AllersSee answer below:
Continuation:
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Elijah AbramTo integrate ( \int \frac{1}{\sqrt{x^2 - 4x - 21}} , dx ) using trigonometric substitution, we first complete the square in the denominator to express it in the form ( \sqrt{a^2 - x^2} ). Then we use the substitution ( x = a \sec(\theta) ), where ( a ) is a constant. After performing the substitution and simplifying, we integrate with respect to ( \theta ) and then revert back to the variable ( x ) 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.
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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