定积分问题,上限3下限-3,∫(1+x)根号(9-x^2)dx

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定积分问题,上限3下限-3,∫(1+x)根号(9-x^2)dx定积分问题,上限3下限-3,∫(1+x)根号(9-x^2)dx定积分问题,上限3下限-3,∫(1+x)根号(9-x^2)dx令x=3sin

定积分问题,上限3下限-3,∫(1+x)根号(9-x^2)dx
定积分问题,上限3下限-3,∫(1+x)根号(9-x^2)dx

定积分问题,上限3下限-3,∫(1+x)根号(9-x^2)dx
令x=3sint
原式=∫(-π/2→π/2)(1+3sint)*3cost*3costdt=∫(-π/2→π/2)9cos^2(t)dt+∫(-π/2→π/2)27sintcos^2(t)dt=9/2∫(-π/2→π/2)(cos(2t)+1)dt-27∫(-π/2→π/2)cos^2(t)d(cost)=9/4sin(2t)|(-π/2→π/2)+9/2t|(-π/2→π/2)-9cos^3(t)|(-π/2→π/2)=0+9/2π-0=4.5π