# How do you evaluate the definite integral #int (1+y^2)/y dy# from #[1,2]#?

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To evaluate the definite integral ∫(1+y^2)/y dy from 1 to 2, you can use the properties of integrals and apply the fundamental theorem of calculus. First, rewrite the integrand as (1/y) + y. Then integrate each term separately. The integral of 1/y is ln|y|, and the integral of y is (1/2)y^2. Evaluate each integral at the upper and lower limits of integration (2 and 1, respectively), and subtract the result of the lower limit from the upper limit.

So, ∫(1+y^2)/y dy from 1 to 2 = [ln|2| + (1/2)(2)^2] - [ln|1| + (1/2)(1)^2] = [ln(2) + 2] - [0 + 1/2] = ln(2) + 3/2.

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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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