f下1上2 [3x+(x^2+2)]dx 怎么算喔?

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f下1上2 [3x+(x^2+2)]dx 怎么算喔?
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f下1上2 [3x+(x^2+2)]dx 怎么算喔?
f下1上2 [3x+(x^2+2)]dx 怎么算喔?

f下1上2 [3x+(x^2+2)]dx 怎么算喔?
f下1上2 [3x+(x^2+2)]dx=3/2x^2﹢1/3x^3+2x|(下一上二)=28/3
(3/2x^2)’=3x ( 1/3x^3)’=x^2 ( 2x)’=2 然后代数算就好了

解:
∫[1,2](3x+x^2+2)dx
=∫[1,2]3xdx+∫[1,2]x^2dx+∫[1,2]2dx
=3/2x^2|[1.2]+1/3x^3|[1,2]+2x|[1,2]
=6-3/2+8/3-1/3+4-2
=9/2+7/3+2
=(27+14+12)/6
=53/6

由积分公式∫x^ndx=x^(n +1)/(n +1)可得原式=〔3x^2/2 x^3/3 2x〕带上下限2.1 结果为53/6.