计算定积分：∫（3,-4）|x|dx ∫（e+1,2）1/（x-1）dx ∫（8,-1）³√xdx

题目

计算定积分：∫（3,-4）|x|dx ∫（e+1,2）1/（x-1）dx ∫（8,-1）³√xdx

答案

∫(-3->4) |x| dx,所求面积都在x轴上面,所以要分区间
= ∫(-3->0) (-x) dx + ∫(0->4) x dx
= -x²/2 + x²/2
= -(-9/2) + 16/2
= 25/2
∫(2->e+1) 1/(x-1) dx
= ln|x-1|
= ln(e+1-1) - ln(2-1)
= lne - ln1
= 1
∫(-1->8) ∛x dx
= x^(1/3+1) / (1/3+1)
= (3/4)x^(4/3)
= (3/4)*8^(4/3) - (3/4)*(-1)^(4/3)
= 12 - 3/4
= 45/4