How do you evaluate: #int_{2}^3 x^2  3 dx#?
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To evaluate the integral ∫_{2}^3 (x^2  3) dx, follow these steps:

Integrate the function (x^2  3) with respect to x. ∫ (x^2  3) dx = (1/3)x^3  3x.

Evaluate the definite integral by substituting the upper limit (3) and the lower limit (2) into the antiderivative and subtracting the result of the lower limit from the upper limit. ∫_{2}^3 (x^2  3) dx = [(1/3)(3)^3  3(3)]  [(1/3)(2)^3  3(2)].

Calculate the values. = [(1/3)(27)  9]  [(1/3)(8) + 6] = [(9  9)  (8/3 + 6)] = [0  (8/3 + 6)] = 8/3  6.

Simplify the result. = 8/3  18/3 = 10/3.
Therefore, the value of the integral ∫_{2}^3 (x^2  3) dx is 10/3.
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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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