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For N equal to 6 rectangles and with end-points on the x-axis of and , what is the width  of each rectangle in the midpoint rule formula?

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Rico Jay Laxa
Rico Jay LaxaLv10
24 Sep 2020

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29 Nov 2020

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Problem 8 a) Use your calculator and left Riemann sums for n = 4 subintervals of equal length, to approximate the area bounded by the curve f(x) = x and the z-axis on the interval [2, 4]. Follow the steps below. i) (10 points) Find A.r, the grid points Ik, and fill in the table. If(tk) Ax= ii) (6 points) Compute the left Riemann sum with two decimal places. b) (12 points] A rectangle is constructed with its base on the x-axis, and its two top vertices on the parabola y = 25 - 22. What are the dimensions of the rectangle with the maximum area?

Let be the region bounded by the curves , , and . Use the Midpoint Rule with to estimate the following quantities.

  1. The area of

  2. The volume obtained by rotating about the x-axis

(a)

If the region shown in the figure is rotated about the -axis to form a solid, use the Midpoint Rule with to estimate the volume of the solid.

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