# What is the integral of #int sec(x)# from 0 to 2?

That improper integral diverges (does not exist).

After getting a definition of improper integral, we would try to find this integral by evaluating both

That is, the integral diverges.

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To find the integral of sec(x) from 0 to 2, you can use the integral formula:

∫ sec(x) dx = ln|sec(x) + tan(x)| + C

Integrating sec(x) from 0 to 2:

∫ sec(x) dx = ln|sec(2) + tan(2)| - ln|sec(0) + tan(0)|

sec(0) = 1, tan(0) = 0, sec(2) and tan(2) are calculated using trigonometric functions.

Then substitute the values into the equation and calculate the result.

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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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