# How do you evaluate the integral #int lnxdx# from #[0,1]#?

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To evaluate the integral of ln(x) from 0 to 1, we use integration by parts. Let u = ln(x) and dv = dx. Then, du = (1/x) dx and v = x.

Applying the integration by parts formula ∫u dv = uv - ∫v du, we have:

∫ln(x) dx = x ln(x) - ∫x (1/x) dx = x ln(x) - ∫dx = x ln(x) - x + C

To evaluate the definite integral from 0 to 1, we substitute the limits of integration:

∫[0,1] ln(x) dx = [1 ln(1) - 1] - [0 ln(0) - 0] = [0 - 1] - [0 - 0] = -1 - 0 = -1

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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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