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数学积分代写 Integral Calculus代写 MATH代写 Exam代写

303

Final Exam

Instructions:

(1) You have 160 minutes to solve this exam.

(3) No notes, books, or any electronic devices can be used during this exam, except: One screen to look at the statements and your webcam to participate of the Zoom exam environment.

(4) If you have connectivity issues, join the Zoom exam environment again as soon as possible.

(5) Please make sure to upload your work for each problem to the correct slot on Gradescope, otherwise the work for that problem will not be visible to the graders.

(6) You do not need to print out the exam problem page. But, make sure to label each solution.

(7) This exam has 7 problems (2 pages). Five of the problems have 2 parts. The total score is 100 points.

(8) Show all your work! Unless otherwise specified, an answer without a full procedure or explanation might receive no credit.

Trigonometric identities:数学积分代写

sin2(θ) + cos2(θ) = 1

tan2(θ) + 1 = sec2(θ)

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ)= cos2(θ)sin2(θ)

cos2(θ) = ½ + ½ cos(2θ)

sin2(θ) = ½ ½ cos(2θ)

(4) (16 points) Problems 4a) and 4b) do not depend on each other and deal with partial fractions. 数学积分代写

(5a) (8 points) Set up, but do not evaluate, an integral which computes the area of the region between the curves y = 12 x2 and y = x2 6.

(5b) (8 points) Set up, but do not evaluate, an integral that computes the arc-length of the upper half of the ellipse 4x2 + y2 = 1.

(6) (16 points) 数学积分代写

Let R be the region between the curves y = x2 and y = 4x.

(6a) (8 points) R is revolved about the x-axis to produce a solid. Set up, but do not evaluate, an integral which computes the volume of this solid. You may use any method you choose, but make sure you state the method you are using.

(6b) (8 points) R is revolved about the line x = 1 to produce a solid. Set up, but do not evaluate, an integral which computes the volume of this solid. You may use any method you choose, but make sure you state the method you are using.

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