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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