利用定积分的定义,计算∫²¹（3x+2）dx的值.急感激不尽!？
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根据定积分定义,得
∫(3x+2)dx
=lim(n->∞){(1/n)[(3(1+1/n)+2)+(3(1+2/n)+2)+(3(1+3/n)+2).+(3(1+n/n)+2)]}
=lim(n->∞){(1/n)[3n+(3/n)(1+2+3+.+n)+2n]}
=lim(n->∞){(1/n)[5n+(3/n)n(n+1)/2]}
=lim(n->∞)[5+(3/2)(1+1/n)]
=5+(3/2)(1+0)
=13/2.,4,
∫(3x+2)dx
=lim(n->∞){(1/n)[(3(1+1/n)+2)+(3(1+2/n)+2)+(3(1+3/n)+2).+(3(1+n/n)+2)]}
=lim(n->∞){(1/n)[3n+(3/n)(1+2+3+.+n)+2n]}
=lim(n->∞){(1/n)[5n+(3/n)n(n+1)/2]}
=lim(n->∞)[5+(3/2)(1+1/n)]
=5+(3/2)(1+0)
=13/2.,4,
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