Question: Question 1 (Essay Worth 10 points) (05.01) Using n = 4 equal-width rectangles, approximate ((x2+8)dx. Use the left end-point of each sub-interval to determine the

determine the height of each rectangle. -2Question 2 (Essay Worth 10 points)

(05.02) Water leaks from a tank at the rate of r(t) gallons

per hour. The rate decreased as time passed, and values of the

rate at two-hour time intervals are shown in the table below. The

total amount of water that leaked out is evaluated by a Riemann

Question 1 (Essay Worth 10 points) (05.01) Using n = 4 equal-width rectangles, approximate ((x2+8)dx. Use the left end-point of each sub-interval to determine the height of each rectangle. -2Question 2 (Essay Worth 10 points) (05.02) Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles. Give your answer with one decimal place. t (hr) 0 2 6 8 10 r(t) (gal/hr) 8.7 7.6 6.8 6.2 5.7 5.3Question 3 (Essay Worth 10 points) (05.03) X. Find the interval on which the curve of y=J D 2 1+3t+t2 dt is concave up. [[2] Question 4 (Essay Worth 10 points) (05.06) COS (X) Evaluate dx . 1+ sin(x)Question 5 (Essay Worth 10 points) (05.06) Evaluate exactly the value of (2x5 +6x) (5x4 +3)dx . Your work must include the use of substitution and the antiderivative

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