Question

定积分求帮助

Answer 1

第一题如图:

第二题如图:

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追答

第二题结果分母4改为16

Answer 2

（1）令x=tant，则dx=sec^2tdt
原式=∫(π/4,π/3) sec^2t/(tan^2t*sect)dt
=∫(π/4,π/3) cost/sin^2tdt
=∫(π/4,π/3) d(sint)/sin^2t
=-1/sint|(π/4,π/3)
=-2/√3+√2
=√2-(2/3)*√3
（2）令x=asint，则dx=acostdt
原式=∫(0,π/2) a^2*sin^2t*acost*acostdt
=a^4*∫(0,π/2) sin^2t*cos^2tdt
=(a^4/4)*∫(0,π/2) sin^2(2t)dt
=(a^4/8)*∫(0,π/2) (1-cos4t)dt
=(a^4/8)*[t-(1/4)*sin4t]|(0,π/2)
=(a^4/8)*(π/2)
=a^4*(π/16)

Answer 3