How do you find the definite integral of #int 1/(x+2)# from [1,1]?
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To find the definite integral of ( \int_{1}^{1} \frac{1}{x+2} ), you can use the fundamental theorem of calculus.

First, find the antiderivative of ( \frac{1}{x+2} ), which is ( \lnx+2 ).

Then, evaluate the antiderivative at the upper and lower limits of integration and subtract the lower limit value from the upper limit value.
( \int_{1}^{1} \frac{1}{x+2} dx = \left[\lnx+2\right]_{1}^{1} = \ln1+2  \ln1+2 = \ln(3)  \ln(1) = \ln(3) )
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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