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The past exam paper of Calculus, key points are: Indefinite, Evaluate, Exact Value, Definite Integral, Compute, Function, Table, Definite Integral, Bounded, Graph
Typology: Exams
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EXAM I - FEBRUARY 4, 2005
Instruction: Read each question carefully. Explain ALL your work and give reasons to support your answers. Advice: DON’T spend too much time on a single problem.
Problems Maximum Score Your Score
1
2 EXAM I - FEBRUARY 4, 2005
1.(10 pts.)(a) Evaluate the indefinite integral ∫ (^) sin( 1 t ) t^2 dt.
(10 pts.)(b) Evaluate the indefinite integral ∫ x cos(2x) dx.
4 EXAM I - FEBRUARY 4, 2005
3.(15 pts.)(a) The region R is bounded by the graph of y = x^3 , the line x = 1 and the axis y = 0. Find the exact volume of the solid formed by revolving the region R about the x-axis.
(5 pts.)(b) Write (DO NOT evaluate) a definite integral representing the arc-length of the path given by y = x^3 from the origin (0,0) to the point (1,1).
MATH106D CALCULUS II - PROF. P. WONG 5 4.(7 pts.)(a) Compute the exact value of the improper integral, if it exists. ∫ (^2) 0
√^ s 4 − s^2
ds
(7 pts.)(b) Compute the exact value of the improper integral, if it exists. ∫ (^) ∞ 0
3 re−r^2 dr
(6 pts.)(c) Determine, by comparison, whether the following improper integral converges or not. Explain briefly. ∫ (^) ∞ 1
e−x^2 dx
