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) ∫ (

sin x + x−1 − 4x5 )

d x

(b) ∫

3x5/3+12x4 6x2 d x

(c) ∫

3x2 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) = x3−6x2+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) = √

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(πx) 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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