课程名称︰微积分乙下 课程性质︰必修 课程教师︰张秀瑜 开课学院：理学院 开课系所︰经济/管院/地理 考试日期（年月日）︰2011/6/21 考试时限（分钟）：110分钟 是否需发放奖励金：请~ （如未明确表示，则不予发放） 试题 : 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 想说今天来po一下~ 试题版首po 如果打得不漂亮的地方敬请见谅 --

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