Question

求定积分x^2+1/x^4 上限2 下限1

答案是21/8,但我始终算出的是63/24，求详细过程

Answer 1

你的答案和参考答案都是正确的，只是你没约分而已。
∫(1→2) (x² + 1/x⁴) dx
= ∫(1→2) [x² + x^(-4)] dx
= [x³/3 + x^(-3)/(-3)] |(1→2)
= (1/3)[x³ - 1/x³] |(1→2)
= (1/3)[(8 - 1/8) - (1 - 1)]
= (1/3)(63/8)
= 63/24，63和24约分，各除以3
= 21/8

Answer 2

∫[1,2] (x^2+1/x^4)dx
=∫[1,2]x^2dx+∫[1,2]x^(-4)dx
=(1/3)x^3|[1,2] +(-1/3)x^(-3)|[1,2]
=(1/3)*7+(-1/3)*(1/8-1)
=7/3+(7/24)
=63/24

Answer 3

[1,2] ∫ (x²+1/x^4) dx
=[x³/3 - 1/(3x³) ] |[1,2]
=(x^6-1)/(3x³) |[1,2]
=63/24
你的答案是正确的