# How do you Use a Riemann sum to find area?

By definition,

by simplifying the expression inside the summation,

by splitting the summation and pulling out constants,

I hope that this was helpful.

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To use a Riemann sum to find the area under a curve, follow these steps:

- Divide the interval over which you want to find the area into subintervals.
- Choose sample points within each subinterval.
- Calculate the function value at each sample point.
- Multiply the function value at each sample point by the width of the subinterval.
- Sum up all these products to get an approximation of the total area under the curve.

As the number of subintervals approaches infinity and the width of each subinterval approaches zero, this approximation becomes more accurate and converges to the actual area under the curve, which is the integral of the function over the given interval.

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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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- 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?
- How do you Use the trapezoidal rule with #n=6# to approximate the integral #int_0^1e^-sqrt(x)dx#?
- What is midpoint Riemann sum?

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