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[3] 5. (a) Let f(T) = 1 + Write the Riemann sum for f over the interval (0, 1) using a uniform partition of (0,1) into 5 equal subintervals and mid-points as your sample points. There is no need to simplify your answer. [3] (b) If f is the function defined by f Jo 2 + sint dt, find f'(2). (c) Sketch the region in the first quadrant bounded by: y==y= VT, 1=1, r=e, and then find its area.

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Nestor Rutherford
Nestor RutherfordLv2
10 Dec 2017
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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?

10. In all of this question let f(x) = -2? + 4.c. (a) Make a small sketch of the region bounded by the r-axis and the curve y = f(1) and then use the Fundamental Theorem of Calculus to find its area. [5 points) (b) Use the definition of the definite integral to find the area of the region in Part (a). Show all of your work. (11 points)

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