求定积分,上限2派,下限0,根号下（1+cosx)de答案为4根号2_数学解答

求定积分,上限2派,下限0,根号下（1+cosx)de答案为4根号2

人气：293 ℃　时间：2020-04-26 21:22:35

解答

√（1+cosx)
=√[1+2cos^2(x/2)-1]
=√[2cos^2(x/2)]
=√2*cos(x/2)
∫[0,π/2]√（1+cosx)dx
=∫[0,π/2]√2*cos(x/2)dx
=2√2sin(x/2)[0,π/2]
=2√2*√2/2
=2