Integration

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2009-08-14 20:44:51 補充：
樓下計錯數了

integrate (-t)[(t^2-1)^(1/3)] with respect to t?

let u = t^2 - 1
du = 2t dt
-1/2 du = -t dt


then

integrate (-t)[(t^2-1)^(1/3)] with respect to t
=integrate [(t^2-1)^(1/3)] (-t) dt
=integrate u^(1/3) (-1/2 )du
=(-1/2 ) / ( 1+ 1/3) * u^(1/3 +1) *= multiplies
= -(2/3)*u^(4/3)
=-(2/3)*(t^2 -1) ^(4/3)

:)