# 10 multiple choice 5 short answers

1.

Use the properties of sigma notation and the summation formulas to evaluate . (5 points)

 235 555 940 1865

2.

Let . Use geometric formulas to evaluate . (5 points)

 18 16 15 None of these

3.

Write the definite integral for the summation: . (5 points)

4.

Find . (5 points)

 6e6x e6x 3e6x

5.

Find an antiderivative of . (5 points)

 x3 + C None of these

6.

Evaluate . (5 points)

 tan(x) + C sec2(x) + C -cot(x) + C None of these

7.

Evaluate the integral . (5 points)

8.

Find the antiderivative of . (5 points)

 None of these Cannot be found

9.

10.

Suppose and , find the value of . (5 points)

 2 4 8 32

1.

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.

t (hr) 0 2 4 6 8 10
r(t) (gal/hr) 10.7 8.6 6.6 5.2 5.0 4.5

3.

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)