已知EX=-1,DX=3,则E[3(X2-2)]=( ).A. 9B. 6C. 30D. 36

描绘下列函数的图形: (1). =dfrac (1)(5)((x)^4-6(x)^2+8x+7);

计算定积分 (int )_(0)^1(2x+1)dx.

、证明:当 -1lt xlt 0 时, arcsin sqrt (1-{x)^2}-arctan dfrac (x)(sqrt {1-{x)^2}}=dfrac (pi )(2) .

求下列各平面的方程-|||-(1)通过点 P(2,0,-1) ,且又通过直线-|||-dfrac (x+1)(2)=dfrac (y)(-1)=dfrac (z-2)(3) 的平面;-|||-(2)通过直线 dfrac (x-2)(1)=dfrac (y+3)(-5)=dfrac (z+1)(-1) 且-|||-与直线 ) 2x-y+z-3=0, x+2y-z-5=0 . 平行的平-|||-面.

2.用极坐标计算下列二重积分:-|||-(1) iint sin sqrt ({x)^2+(y)^2}dxdy, 其中 = (x,y)|{n)^2leqslant (x)^2+(y)^2leqslant 4(pi )^2} ;

2.求下列不定积分(其中a,b,w,φ均为常数):-|||-(1)int (e)^5tdt;-|||-(2) int ((3-2x))^3dx ;-|||-(3) int dfrac (dx)(1-2x) =-|||-(4) int dfrac (dx)(sqrt [3]{2-3x)} :-|||-(5) int (sin ax-(e)^dfrac (x{b)})dx ;-|||-(6) int dfrac (sin sqrt {t)}(sqrt {t)}dt =-|||-(7) int x(e)^-(x^2)dx ;-|||-(8)int xcos ((x)^2)dx;-|||-(9) int dfrac (x)(sqrt {2-3{x)^2}}dx :-|||-(10) int dfrac (3{x)^3}(1-{x)^4}dx :-|||-(11) int dfrac (x+1)({x)^2+2x+5}dx ;-|||-(12) int (cos )^2(omega t+varphi )sin (omega t+varphi )dt ;-|||-(13) int dfrac (sin x)({cos )^3x}dx =-|||-(14) int dfrac (sin x+cos x)(sqrt [3]{sin x-cos x)}dx :-|||-(15)int (tan )^10xcdot (sec )^2xdx;-|||-(16) int dfrac (dx)(xln xln ln x)-|||-(17) int dfrac (dx)({(arcsin x))^2sqrt (1-{x)^2}} :-|||-__-|||-(18) int dfrac ({10)^2arcsin x}(sqrt {1-{x)^2}}dx :

6. 讨论方程 ln x=ax, (其中 gt 0 )有几个实根?

3.利用极坐标计算下列二重积分:-|||-(1) iint sqrt ({x)^2+(y)^2}dtheta D是由 ^2+(y)^2=1 围成的区域;-|||-(2) iint sqrt (4-{x)^2-(y)^2}dtheta D是由 ^2+(y)^2=4 围成的区域,且 geqslant 0 geqslant 0 ;-|||-(3) iint ((x)^2+(y)^2)db D是由 ^2+(y)^2-2x=0(ygeqslant 0) 与x轴所围成的区域.-|||-b

对数曲线y=lnx上哪一点处的曲率半径最小？求出该点处的曲率半径.

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