∫(上限是1,下限是0)x^2√1-x^2dx
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令x=sint, 则dx=costdt
原式=∫(0, π/2) (sint)^2(cost)^2dt
=∫(0,π/2)(sintcost)^2dt
=1/4∫(0,π/2)(sin2t)^2dt
=1/8∫(0,π/2)(1-cos4t)dt
=1/8(t-1/4sin4t)|(0,π/2)
=1/8(π/2)
=π/16
原式=∫(0, π/2) (sint)^2(cost)^2dt
=∫(0,π/2)(sintcost)^2dt
=1/4∫(0,π/2)(sin2t)^2dt
=1/8∫(0,π/2)(1-cos4t)dt
=1/8(t-1/4sin4t)|(0,π/2)
=1/8(π/2)
=π/16
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