为自己加油

计算定积分：
∫^π/2₀e^xcosxdx

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)．