9.用图像表示下列定积分:

(1)∫_1^2▒ log2xdx;(2)∫_2^6▒ xdx.

解(1)∫_1^2▒ log2xdx表示曲线y=log2x,直线x=1,x=2及x轴围成的曲边梯形的面积,如图①中阴影部分所示.

①

②

　　(2)∫_2^6▒ xdx表示直线y=x,x=2,x=6及x轴围成的直角梯形的面积,如图②中阴影部分所示.

10.导学号88184046利用定积分的性质求∫_("-" 1)^1▒ (2x/(x^4+1)┤+├ sin^3 x"-" (e^x "-" 1)/(e^x+1))dx.

解y=2x/(x^4+1),y=sin3x显然均为[-1,1]上的奇函数.

　　而对f(x)=(e^x "-" 1)/(e^x+1),

　　∵f(-x)=(e^("-" x) "-" 1)/(e^("-" x)+1)=(1"-" e^x)/(1+e^x )=-f(x),

　　∴函数f(x)=(e^x "-" 1)/(e^x+1)为奇函数.

　　∴∫_("-" 1)^1▒ 2x/(x^4+1)dx=0,∫_("-" 1)^1▒ sin3xdx=0,∫_("-" 1)^1▒ (e^x "-" 1)/(e^x+1)dx=0.

　　∴∫_("-" 1)^1▒ (2x/(x^4+1)+sin^3 x"-" (e^x "-" 1)/(e^x+1))dx=∫_("-" 1)^1▒ 2x/(x^4+1)dx+ ∫_("-" 1)^1▒ sin3xdx-∫_("-" 1)^1▒ (e^x "-" 1)/(e^x+1)dx=0.

B组

1.设f(x)={■(x^2 "," x≥0"," @2^x "," x<0"," )┤则∫_("-" 1)^1▒ f(x)dx的值为(　　)

A.∫_("-" 1)^1▒ x2dx B.∫_("-" 1)^1▒ 2xdx

C.∫_("-" 1)^0▒ x2dx+∫_0^1▒ 2xdx D.∫_("-" 1)^0▒ 2xdx+∫_0^1▒ x2dx