所屬科目：研究所、轉學考(插大)-微積分
【試題 1】(10 分) Evaluatedx.
【試題 3】(15 分) Let R be the region bounded by the square with vertices (0， 1)， (1， 2)， (2， 1)， (1， 0). Evaluate the integral dA.
【試題 4】(15 分) Evaluate， where C is the parabolic arc given by y = 4x - x² from (4， 0) to (1， 3).
【試題 5】(20 分) Let S be the region bounded by the cylinder: x² + y² = 4， 0 ≤ z ≤ 1. Find the outward flux of the vector field through the cylinder.
【試題 6】(20 分) Use Green's theorem to evaluate the line integral
where C is the boundary of the region defined by x = 0， y = 0， and x + y = 1.
(a) (5 分) Let be a force， calculate the work done in the displacement along the helix C: from A(2， 0， 0) to B(0， 2， 3π).
(b) (5 分) What is ds， where C is the arc of the helix x = cost， y = sint， z = t， which joins the points (1， 0， 0) and (-1， 0， π)?
阿摩線上測驗
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阿摩線上測驗
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dx.
dA.
， where C is the parabolic arc given by y = 4x - x² from (4， 0) to (1， 3).
through the cylinder.
be a force， calculate the work done in the displacement along the helix C:
from A(2， 0， 0) to B(0， 2， 3π).
ds， where C is the arc of the helix x = cost， y = sint， z = t， which joins the points (1， 0， 0) and (-1， 0， π)?