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研究所、轉學考(插大)-微積分
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99年 - 99 國立政治大學轉學生招生考試_應用數學系：微積分(二)#122370
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題組內容
1. Evaluate the following integrals:
(b) (5%) ∫
dx
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(a) (5%) ∫ dx
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5. (15%) Evaluate the following integral along the curve C = {(x,y,z) ∈ R³ | x² + y² = 4, z = -3}, oriented counterclockwise as seen by a person standing at the origin and with respect to the right-handed Cartesian coordinates, where F = yi + xz³j – zy³k, r' = dr/ds is the unit tangent vector, and *sis the arc length of C
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6. (15%) Evaluate the following integral I = ∫L(2xyz²) dx + (x²z² + z cos(yz)) dy + (2x²yz + y cos(yz)) dzalong the line segment L from P: (0,0,1) to Q: (2,π/4,2)
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dx
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dx