# How do you evaluate the integral #int x dx# from #-oo# to #oo# if it converges?

We have:

Integrating:

We can't technically "plug in" infinity and negative infinity, so take their limits:

Both approach positive infinity:

graph{x [-304.4, 304.4, -152.2, 152.2]}

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If the integral ∫x dx from -∞ to ∞ converges, it can be evaluated using techniques from calculus. Since the integral represents the area under the curve of the function x from negative infinity to positive infinity, it converges if the function x approaches zero sufficiently quickly as x tends to positive or negative infinity. The integral evaluates to zero if the function x is odd, and it diverges if the function x is even. If the integral converges, it can be evaluated using methods such as integration by parts or 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.

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