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frzb0171

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i need solve this 2 exams to study them i need get an A on both.

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Math 156 Exam 1 - Version A 1. Evaluate the following integrals. Z sin(e 2x + 1) (a) dx e2x (b) Z [10] 4t + 5 dt t2 + 9 [12] Page 1 of 6 Math 156 (c) Z (d) Z Exam 1 - Version A cot(2x) dx 4 0 p [10] 3x dx 9 + x2 [13] Page 2 of 6 Math 156 Exam 1 - Version A 2. (a) Sketch the region bounded by the curves y = 3 x2 , y = 1 x, and y = 2. (b) Set up but do not evaluate an integral that computes the area bounded by the curves y = 3 x2 , y = 1 x, and y = 2. Page 3 of 6 [5] [10] Math 156 Exam 1 - Version A 3. (a) Sketch the region enclosed by the curves y = p x 1, y = 1, and x = 3. (b) Use the method of cylindrical shells to write down p an integral for the volume of the solid obtained by rotating the region enclosed by y = x 1, y = 1, and x = 3 about the x-axis. Do not evaluate the integral. Page 4 of 6 [5] [10] Math 156 Exam 1 - Version A 4. (a) Sketch the region enclosed by the curves y = x2 and x = y 2. (b) Use the method of washers to write down an integral for the volume of the solid obtained by rotating the region enclosed by y = x2 and x = y 2, about the line y = 4. Do not evaluate the integral. Page 5 of 6 [5] [10] Math 156 Exam 1 - Version A 3 2 5. Set up but do not p evaluate an integral that computes the arc length of the curve 4y = 9x from (0, 0) to (2 3, 3). p 6. (BONUS) Compute the arc length of the above curve 4y 3 = 9x2 from (0, 0) to (2 3, 3). Page 6 of 6 [10] [3 (bonus)] Math 156 Exam 1 - Version B 1. Evaluate the following integrals. Z 3 4x p (a) dx 25 x2 0 (b) Z cos(e 3t e3t + 2) [13] dt [10] Page 1 of 6 Math 156 Exam 1 - Version B (c) Z 3x + 5 dx x2 + 4 [12] (d) Z cot(5x) dx [10] Page 2 of 6 Math 156 Exam 1 - Version B 2. (a) Sketch the region bounded by the curves y = x2 3, x + y = 1, and y = 2. (b) Set up but do not evaluate an integral that computes the area bounded by the curves y = x2 3, x + y = 1, and y = 2 Page 3 of 6 [5] [10] Math 156 Exam 1 - Version B 3. (a) Sketch the region enclosed by the curves y = p x + 1, y = 1, and x = 2. (b) Use the method of cylindrical shells to write down p an integral for the volume of the solid obtained by rotating the region enclosed by y = x + 1, y = 1, and x = 2 about the x-axis. Do not evaluate the integral. Page 4 of 6 [5] [10] Math 156 Exam 1 - Version B 4. (a) Sketch the region enclosed by the curves y = x2 + 1 and x = y 3. (b) Use the method of washers to write down an integral for the volume of the solid obtained by rotating the region enclosed by y = x2 + 1 and x = y 3 about the line y = 5. Do not evaluate the integral. Page 5 of 6 [5] [10] Math 156 Exam 1 - Version B 5. Set up but do notpevaluate an integral that computes the arc length of the curve 9y 2 = 4x3 from (0, 0) to (3, 2 3). p 6. (BONUS) Compute the arc length of the curve 9y 2 = 4x3 from (0, 0) to (3, 2 3). Page 6 of 6 [10] [3 (bonus)]
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