计算下列定积分的值:(1)求 (x-1)的五次方在区间[1,2]的定积分;(2)求 (x+sinx)在区间[0,π/2]的定积分.
网友回答
∫(1→2) (x - 1)⁵ dx
= ∫(1→2) (x - 1)⁵ d(x - 1)
= (1/6)(x - 1)⁶ |(1→2)
= (1/6)(2 - 1)⁶
= 1/6∫(0→π/2) (x + sinx) dx
= (x²/2 - cosx) |(0→π/2)
= (π²/4*1/2 - 0) - (0 - 1)
= 1 + π²/8
======以下答案可供参考======
供参考答案1:
1)1/62)π^2/8+1