[試題] 99下 張秀瑜 微積分乙下 期末考

[jech801127 (cosmos)]

課程名稱︰微積分乙下
課程性質︰必修
課程教師︰張秀瑜
開課學院：理學院
開課系所︰經濟/管院/地理
考試日期（年月日）︰2011/6/21
考試時限（分鐘）：110分鐘
是否需發放獎勵金：請~
（如未明確表示，則不予發放）

試題 :

          yx^2
1.(a)∫∫________ dA   R=[0,1] ×[0,3]  (10%)
       R  x^3+1

      1 2  xe^x
  (b)∫∫_______ dydx   (10%)
      0 1   y


2.(10%)Find the volumn of the solid under the plane x+y-z=0 and above the
       triangle with vertices (1,1), (4,1) and (1,2)

3.Sketch the region and evaluate the integral by reversing the order of
  integration

       1   π/2
  (a) ∫   ∫   cosx(1+cosx^2)^1/2 dxdy (10%)
       0  arcsiny


       1 1
  (b) ∫∫cos(y^2)dydx                  (10%)
       0 x
                 3 (9-x^2)^1/2
4.(10%)Evaluate ∫∫(x^2+y^2)^1/2 dydx by converting to polar cordinates.
                -3 0


5.(10%)Find the mass of the solid E={(x,y,z) 0≦x≦1 0≦y≦x x≦z≦2x}
       with the density function p(x,y,z)=yzcos(x^5)


6.(10%)Evaluate ∫∫∫ (x^2 + y^2 + z^2)dV , where E:  0 ≦ z ,
                   E

   x^2 + y^2 + z^2 ≦ 1


7.(10%)Find the image of the set S={(u,v) 3≧u≧0, 2≧v≧0} of the
       transformation x=2u+3v, y=u-v


                        y-x
8.(10%)Evaluate ∫∫cos ___ dA, where R is the trapezoidal region with
                  R     y+x

       vertices (1,0), (2,0), (0,2), (0,1)


用了一年的板 想說今天來po一下~
試題版首po 如果打得不漂亮的地方敬請見諒

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