企源知识库

求∫_π/2⁰x²sinxdx．
【正确答案】：∫₀^π/2sinxdx =-∫₀^π/2x²dcosx =-x²cosx|₀^π/2+∫₀^π/2cosxdx² =0+∫₀^π/22xcosxdx =2∫₀^π/2xdsinx =2xsinx|₀^π/2-2∫₀^π/2sinxdx =π-2(-cosx)|₀^π/2=π-2．