微积分 ..计算∫[π/6,0]dy ∫[π/6,y] (cosx)/x dx0.5

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微积分..计算∫[π/6,0]dy∫[π/6,y](cosx)/xdx0.5微积分..计算∫[π/6,0]dy∫[π/6,y](cosx)/xdx0.5微积分..计算∫[π/6,0]dy∫[π/6,y

微积分 ..计算∫[π/6,0]dy ∫[π/6,y] (cosx)/x dx0.5
微积分 ..计算∫[π/6,0]dy ∫[π/6,y] (cosx)/x dx
0.5

微积分 ..计算∫[π/6,0]dy ∫[π/6,y] (cosx)/x dx0.5
此题必须交换积分顺序才能求出结果!
根据题意,知积分区域是由y=x,x=π/6,y=0所围成的
故 原式=∫(π/6,0)(cosx/x)dx∫(x,0)dy
=∫(π/6,0)(cosx/x)(x-0)dx
=∫(π/6,0)cosxdx
=(sinx)|(π/6,0)
=1/2-0
=1/2