计算定积分：∫π/20excosxdx

2024-09-16 09:59:36
高等数学（二）(z0002)

计算定积分：
∫^π/2₀e^xcosxdx
【正确答案】：由∫^π/2₀e^xcosxdx=∫^π/2₀cosxd(e^x)=[e^xcosx]^π/2₀ +∫^π/2₀e^xsinxdx =-1+[e^xsinx]^π/2₀-∫^π/2₀e^xcosxdx=e^π/2-1-∫^π/2₀e^xcosxdx，故 ∫^π/2₀e^xcosxdx=1/2(e^π/2-1)．

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