【答案】C

5.如图所示,曲线y=f(x)与直线x=a,x=b,y=0围成的阴影部分的面积S为　　　　.

　　【解析】如图所示,在区间[a,c)上,f(x)<0;在区间[c,b]上,f(x)≥0.

　　所以所求阴影部分的面积S=-∫_a^c▒ f(x)dx+∫_c^b▒ f(x)dx.

　　【答案】S=-∫_a^c▒ f(x)dx+∫_c^b▒ f(x)dx

6.若a=∫_0^(π/4)▒x dx"," b=∫_0^(π/4)▒sin xdx"," c=∫_0^(π/4)▒ tan xdx,则三者之间的大小关系为　　　　.

　　【解析】当x∈(0"," π/4)时,sin x

　　【答案】b

7.已知函数f(x)={■(x"," x"∈[" 0"," 2")," @4"-" x"," x"∈[" 2"," 3")," @5/2 "-" x/2 "," x"∈[" 3"," 5"]." )┤

求f(x)在区间[0,5]上的定积分.

　　【解析】由题意可知函数f(x)的图象如图所示.由定积分的几何意义,知

　　∫_0^2▒ xdx=1/2×2×2=2,

　　∫_2^3▒ (4-x)dx=1/2×(1+2)×1=3/2,

　　∫_3^5▒ (5/2 "-" x/2)dx=1/2×2×1=1,

　　故∫_0^5▒ f(x)dx=∫_0^2▒ xdx+∫_2^3▒ (4-x)dx+∫_3^5▒ (5/2 "-" x/2)dx=2+3/2+1=9/2.

拓展提升(水平二)

8.已知t>0,若∫_0^t▒ (2x-2)dx=8,则t=(　　).

　　A.1 B.-2 C.-2或4 D.4

【解析】函数f(x)=2x-2的图象如图所示,与x轴交于点A(1,0),与y轴交于点B(0,-2),易求得S△OAB=1.