# How do you test the improper integral #int (x^2+2x-1)dx# from #[0,oo)# and evaluate if possible?

The integral is divergent. See explanation.

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See process below

Think about geometrical meaning of integral: "is the area under the curve".

Now, try to evaluate

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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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