=∫_0^3▒ (-8x3)dx+∫_0^3▒ 21x2dx+∫_0^3▒ (-12x)dx+∫_0^3▒ 15dx

　　=-8∫_0^3▒ x3dx+21∫_0^3▒ x2dx-12∫_0^3▒ xdx+15∫_0^3▒ 1dx . ]

　　=-8×81/4+21×9-12×9/2+15×3=18.

★11.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

如图,由定积分的意义,得

　　∫_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, ]

　　所以∫_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.