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1.Use the properties of sigma notation and the summation formulas to evaluate . (5 points)23555594018652.Let . Use geometric formulas to evaluate . (5 points)181615None of these3.Write the definite integral for the summation: . (5 points)4.Find . (5 points)6e6xe6x3e6x5.Find an antiderivative of . (5 points)x3 + CNone of these6.Evaluate . (5 points)tan(x) + Csec2(x) + C-cot(x) + CNone of these7.Evaluate the integral . (5 points)8.Find the antiderivative of . (5 points)None of theseCannot be found9.Use your calculator to evaluate . Give 3 decimal places for your answer. (5 points) 10.Suppose and , find the value of . (5 points)248321.Using n = 4 equal-width rectangles, approximate . Use the mid-point of each sub-interval to determine the height of each rectangle. (10 points)2.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. (10 points)
t (hr)0246810r(t) (gal/hr)10.78.66.65.25.04.53.Find the interval on which the curve of is concave up. (10 points)4.Evaluate . (10 points)5.Evaluate exactly the value of . Your work must include the use of substitution and the antiderivative. (10 points)