How do you test the improper integral #int (2x-1)^-3dx# from #(-oo,0]# and evaluate if possible?
Integrate by substitution and evalute.
So,
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To test and evaluate the improper integral (\int_{-\infty}^{0} (2x - 1)^{-3} dx), we can use the limit definition of improper integrals.
First, determine the limit as (a) approaches (-\infty) of (\int_{a}^{0} (2x - 1)^{-3} dx). Then, evaluate this limit if possible.
The integral converges if the limit exists and diverges if the limit does not exist or is infinite.
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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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