Integrate x^2 between the limits of x = 2 and x = 3

Calculate the definite integral of x^2 with respect to x over the interval from x = 2 to x = 3. This involves finding the area under the curve of the function x^2 between the specified limits. To do this, we first need to find the antiderivative of x^2, which is (1/3)x^3. 

Next, we evaluate the antiderivative at the upper limit of 3 and subtract the result from the evaluation at the lower limit of 2. Plugging in x = 3 into (1/3)x^3 gives us (1/3)(3)^3 = 9, and plugging in x = 2 gives us (1/3)(2)^3 = 8/3. 

Finally, subtracting the result at x = 2 from the result at x = 3 gives us 9 – 8/3 = 19/3. Therefore, the definite integral of x^2 between x = 2 and x = 3 is 19/3, which represents the area under the curve of the function x^2 over the specified interval.

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