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) ? (

sin x + x?1 ? 4×5 )

d x

(b) ?

3×5/3+12×4 6×2 d x

(c) ?

3×2 x3+3 d x

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Name MATH 109 – Midterm Exam 2 Section

2. Given the following graph of f , evaluate ? 2 ?5

f (x)d x

?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?6×2+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) = ?

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 ? 2×2 ? 39. Determine the area of the shaded region. (Use a graphing utility to determine any relevant points of intersection.)