# What is the integral from 0 to 4 of lnx dx?

Let's introduce the idea of improper integrals. Remember that integrals are based on the sums of the individual terms as shown in the Sigma notation below:

Now we can do the math using Eqs. 1 and 3 and split the limit:

Hopefully it makes sense with such a long text!

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The integral from 0 to 4 of ln(x) dx is equal to 4 ln(4) - 4.

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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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- How do you integrate #(sec(x)^2-1)(sin(x)/cos(x))#?
- How do you evaluate the definite integral #int sqrt(2/x)dx# from [1,8]?

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