Math Calculus

Name MATH 109 - Midterm Exam 2 Section

Be sure to show all work for full credit. All answers must be exact values unless otherwise specified. No

rough drafts.

1. Determine the following indefinite integrals.

(a)

R 

sin x + x????1 ???? 4

x5



dx

(b)

R

3x5=3+12x4

6x2 dx

(c)

R

3x2

x3+3dx

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Name MATH 109 - Midterm Exam 2 Section

2. Given the following graph of f , evaluate

R 2

????5 f (x)dx

????4 ????2 2 4

????4

????2

2

4

3. Determine the volume of the solid created by revolving the area bounded by the function f (x) = x3????6x2+12x????7

on the interval x[1; 3] and y = 0, around the x-axis. (Hint: Start by roughly sketching the area to be revolved.)

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Name MATH 109 - Midterm Exam 2 Section

4. Determine the volume of the solid created by revolving the area bounded by f (x) =

p

x ???? 3 on the interval

x[3; 7] and y = 0 about the y-axis. (Hint: Start by roughly sketching the area to be revolved.)

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Name MATH 109 - Midterm Exam 2 Section

5. The figure below shows the graphs of f (x) = 4 + cos(x) and g (x) = 20x ???? 2x2 ???? 39. Determine the area of the

shaded region. (Use a graphing utility to determine any relevant points of intersection.)

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