How do you evaluate #intdx/(1+x^2)# from 0 to 1?
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To evaluate (\int_{0}^{1} \frac{dx}{1+x^2}), we can use the arctangent integral formula.
The integral of (\frac{1}{1+x^2}) with respect to (x) is (\arctan(x)).
Thus, evaluating the definite integral from (0) to (1), we get:
[\int_{0}^{1} \frac{dx}{1+x^2} = \left[\arctan(x)\right]_{0}^{1} = \arctan(1) - \arctan(0)]
Since (\arctan(1) = \frac{\pi}{4}) and (\arctan(0) = 0), we have:
[\int_{0}^{1} \frac{dx}{1+x^2} = \frac{\pi}{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.
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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