# How do you find the Riemann sum for #f(x)=sinx# over the interval #[0,2pi]# using four rectangles of equal width?

So, for this question we get:

and so on.

To go any further and get the same answers, we would need to agree on what to use for sample points.

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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.

- How do you use Riemann sums to evaluate the area under the curve of #f(x) = (e^x) − 5# on the closed interval [0,2], with n=4 rectangles using midpoints?
- How do you determine the area enclosed by an ellipse #x^2/5 + y^2/ 3# using the trapezoidal rule?
- How to you approximate the integral of # (t^3 +t) dx# from [0,2] by using the trapezoid rule with n=4?
- How do you use the Trapezoidal rule and three subintervals to give an estimate for the area between #y=cscx# and the x-axis from #x= pi/8# to #x = 7pi/8#?
- What is Integration Using the Trapezoidal Rule?

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