# How do you evaluate the definite integral #int 2/sqrt(1+x)# from #[0,1]#?

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To evaluate the definite integral ∫(2/√(1+x)) dx from 0 to 1, you can use the substitution method. Let u = 1 + x. Then, du = dx.

So, when x = 0, u = 1, and when x = 1, u = 2.

The integral becomes: ∫(2/√u) du from 1 to 2.

This integrates to: 4√u evaluated from 1 to 2.

Substituting the limits, we get: 4√2 - 4√1.

Which simplifies to: 4√2 - 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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