Math1432Test2.pdf - Print Test PRINTABLE VERSION Test 2 You scored 35 out of 60 Question 1 Your answer is CORRECT Which of the following integrals will

Math1432Test2.pdf - Print Test PRINTABLE VERSION Test 2 You...

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Unformatted text preview: 12/11/2019 Print Test PRINTABLE VERSION Test 2 You scored 35 out of 60 Question 1 Your answer is CORRECT. Which of the following integrals will find the area between 2 f (x) = 4 − x and g(x) = 9 + 6 x ? −1 a) 2 ∫ [ (6 x + 9) − (4 − x ) ] dx −5 −1 b) 2 ∫ [ (4 − x ) − (6 x + 9) ] dx −5 5 c) 2 ∫ [ (4 − x ) − (6 x + 9) ] dx 1 −1 d) 2 ∫ [ (6 x + 9) − (4 − x ) ] dx 0 5 e) 2 ∫ [ (6 x + 9) − (4 − x ) ] dx 1 Question 2 Your answer is CORRECT. Given that the average value of a function f (x) over the interval [0, 4] is a) b) 13 3 4 , find ∫ f (x) dx . 0 12 13 52 3 1/8 12/11/2019 c) d) e) Print Test 26 3 13 13 12 Question 3 Your answer is INCORRECT. The graph of f (x) is shown below on the interval [−2, 1]. The area bounded between the graph of f (x) and the x-axis on [−2, −1] is graph of f (x) and the x-axis on [−1, 0] is on [0, 1] is a) b) 27 4 3 4 3 4 , the area bounded between the , and the area bounded between the graph of f (x) and the x-axis . Determine the average value of f (x) on the interval [−2, 1]. 1 2 9 4 2/8 12/11/2019 c) d) e) Print Test 27 4 11 − 4 15 2 Question 4 Your answer is INCORRECT. The base of a solid is the region bounded by y = x − 8 and y the cross sections perpendicular to the x-axis are squares. 2 = −7 . Find the volume of the solid given that 1 a) 2 ∫ π (1 − x ) 2 dx −1 1 b) 2 ∫ 2 (−15 − x ) dx −1 1 c) 2 ∫ 2 (1 − x ) dx −1 1 d) ∫ π (x 2 2 + 1) dx −1 1 e) ∫ (x 2 2 + 1) dx −1 Question 5 Your answer is INCORRECT. The region bounded by solid generated. a) b) c) f (x) = x 2 and g(x) = √x is revolved around the y-axis. Compute the volume of the 27π 70 3π 10 8π 3 3/8 12/11/2019 d) e) Print Test 3π 5 π 3 Question 6 Your answer is INCORRECT. Let be a region in the first quadrant with centroid (4, 6) and area 12, which does not intersect the line x Find the volume of the solid formed when this region is rotated about the line x = 1. a) 120π b) 72π c) 70π d) 121π e) 69π = 1 . Question 7 Your answer is CORRECT. Find the arc length of a) b) c) + ‾ √3 2 from x π = 0 to x = 6 . ∣ + 2 ∣ 3 2√3 ‾ 3 1 2 d) ln ∣ ∣ e) ln ∣ ∣ f) ‾ √3 ln ∣ ∣ f (x) = ln(cos(x)) + 2 2√3 ‾ + ‾ √3 3 ‾ √3 2 3 + ‾ √3 3 ∣ ∣ ∣ ∣ ‾ √3 3 4/8 12/11/2019 g) Print Test ln ∣ ∣ 2√3 ‾ 3 ∣ + √3 ‾∣ + 2 Question 8 Your answer is CORRECT. Give the formula that will find the surface area of the region formed by revolving x = 2 to x = 6 about the x -axis. f (x) = sin(2 x) from 6 a) ∫ √ ‾‾‾‾‾‾‾‾‾‾‾‾ 2 ‾ 1 + 2 cos (2x) dx 2 6 b) ∫ √ ‾‾‾‾‾‾‾‾‾‾‾‾ 2 ‾ 1 + 4 cos (2x) dx 2 6 c) ∫ ‾‾‾‾‾‾‾‾‾‾‾‾ 2 ‾ 2π sin(2 x) 1 + 4 cos (2x) dx √ 2 6 d) ∫ π sin(2 x)√‾ 1‾‾‾‾‾‾‾‾‾‾‾ + 2 cos(2 x) ‾ dx 2 6 e) ∫ ‾‾‾‾‾‾‾‾‾‾‾‾ 2 ‾ 2π sin(2 x) 1 + 2 cos (2x) dx √ 2 Question 9 Your answer is CORRECT. Give the general solution of y ′ x y + 2y = 2 y 2 a) y b) y c) y d) y e) y 2 2 + 4 ln |y| = 2x + 2 ln |y| = x 2 1 + ln |y| = x 2 2 + 1 + 8x + C + 4x + C + 2x + C 2 2 2 + 2 ln |y| = x 3 + 4x 2 + C + ln |y| = 2x − 2x + C Question 10 5/8 12/11/2019 Print Test Your answer is CORRECT. Find a specific solution for dy − (2 + y)x 2 = 0 dx given that a) y(−2) = −1 1 1 = x 2 + y 2 3 8 + 3 1 3 3 8 b) y c) ∣ ln∣ ∣2 + y∣ = d) ∣ y − 2 ln∣ ∣2 + y∣ = e) ln∣2 + y∣ = ∣ ∣ = x . + 3 3 1 x 3 8 + 3 3 1 x 3 1 x 3 + 1 3 8 − 3 3 Question 11 Your answer is CORRECT. A 300-liter tank initially full of water develops a leak at the bottom. Given that 30% of the water leaks out in the first 7 minutes, give a formula for the amount of water left in the tank t minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present. 7 ln(7/10) t a) A(t) = 210 e b) A(t) = 300 e c) A(t) = 210 e d) A(t) = 300 e e) A(t) = 210 e f) A(t) = 300 e (ln(7/10)) 7 (ln(7/10)) 7 t t ln(10/7) t ln(7/10) t 7 ln(7/10) t 6/8 12/11/2019 Print Test Question 12 Your answer is INCORRECT. Which of the following integrals are improper integrals? ∞ I. ∫ 1 x 0 2 dx + 9 5 II. ∫ x dx 2 ‾‾‾‾‾ ‾ − 9 √x 3 1 III. ∫ 3 dx 3 −1 √x 2 IV. −3 x ∫ e dx 0 a) I only b) I, II and III c) II and IV d) III only e) I and II f) All of the integrals are improper Question 13 Your answer is CORRECT. This is a written question, worth 15 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1334 Evaluate the following integrals if possible. If the integral is improper, re-write it in proper limit notation and evaluate. 2 Part a: (5 points) ∫ ∫ 3 x 1 4 Part b: (5 points) 4x e√ − 6 2 dx x dx 0 √x 7/8 12/11/2019 Print Test ∞ Part c: (5 points) ∫ 0 1 x 2 dx + 4 a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 14 Your answer is CORRECT. This is a written question, worth 25 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1462 A region is bounded by y = e , the x-axis, the y-axis and the line x = 2. −2x Part a: (3 pts) Graph the region and label the points of intersection. Part b: (7 pts) Find the area of this region. Part c: (5 pts) If the region is the base of a solid such that each cross section perpendicular to the x-axis is a square, set up the integral that would find the volume of that solid. Part d: (5 pts) If this region is rotated around the x-axis, set up the integral that would find the volume of the solid generated. Part e: (5 pts) If this region is rotated around the y-axis, set up the integral that would find the volume of the solid generated using the Shell Method. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. 8/8 ...
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