-3到3（x+√9-x^2）dx=
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令x=3sint
x：-3→3，则t：-π/2→π/2
∫[-3：3][x+√(9-x²)]dx
=∫[-π/2：π/2][3sint+√(9-9sin²t)]d(3sint)
=2∫[0：π/2]9cos²tdt
=9∫[0：π/2](1+cos2t)dt
=9(t+½sin2t)|[0：π/2]
=9[(π/2 +½sinπ)-(0+½sin0)]
=9π/2
x：-3→3，则t：-π/2→π/2
∫[-3：3][x+√(9-x²)]dx
=∫[-π/2：π/2][3sint+√(9-9sin²t)]d(3sint)
=2∫[0：π/2]9cos²tdt
=9∫[0：π/2](1+cos2t)dt
=9(t+½sin2t)|[0：π/2]
=9[(π/2 +½sinπ)-(0+½sin0)]
=9π/2
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