计算定积分:∫1-1|x2-3x|dx
当-1≤x≤0时,|x2—3x|=x2-3x;当0≤x≤1时,|x2-3x|=-(x2-3x)=3x-x2故∫1-1x2-3x|dx=∫0-1(x2-3x)dx+∫10(3x-x2)dx=[(1/3)x3-(3/2)x2]0-1+[(3/2)x2-(1/3)x3]10=3.
计算定积分:∫1-1|x2-3x|dx
当-1≤x≤0时,|x2—3x|=x2-3x;当0≤x≤1时,|x2-3x|=-(x2-3x)=3x-x2故∫1-1x2-3x|dx=∫0-1(x2-3x)dx+∫10(3x-x2)dx=[(1/3)x3-(3/2)x2]0-1+[(3/2)x2-(1/3)x3]10=3.