# How do you find an approximation to the integral #int(x^2-x)dx# from 0 to 2 using a Riemann sum with 4 subintervals, using right endpoints as sample points?

I will use what I think is the usual notation throughout this solution.

So

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The approximation to the integral ( \int_{0}^{2} (x^2 - x) , dx ) using a Riemann sum with 4 subintervals and right endpoints as sample points is ( \frac{1}{4}[(1)^2 - (1)] \cdot \frac{2}{4} + [(1.5)^2 - (1.5)] \cdot \frac{2}{4} + [(2)^2 - (2)] \cdot \frac{2}{4} ). This simplifies to ( \frac{1}{4} + \frac{9}{8} + 1 ), which equals ( \frac{15}{4} ).

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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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