# How do you evaluate the definite integral #int (2x-1) dx# from [1,3]?

## 6

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To evaluate the definite integral (\int_{1}^{3} (2x - 1) , dx), you first need to find the antiderivative of the function (2x - 1), which is (x^2 - x). Then, evaluate this antiderivative at the upper limit (3) and subtract the result from the evaluation of the antiderivative at the lower limit (1). This yields:

[\left[ x^2 - x \right]_{1}^{3} = (3^2 - 3) - (1^2 - 1) = (9 - 3) - (1 - 1) = 6 - 0 = 6.]

So, the value of the definite integral (\int_{1}^{3} (2x - 1) , dx) is 6.

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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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