Question

根号(t(1-t))的积分怎么算

Answer 1

∫√(t(1-t)dt
=∫√sin^2x(1-sin^2x)d(sin^2x).令t=sin^2x
=∫2sin^2xcos^2xdx
=∫sin^2(2x)dx/2
=∫[1-cos(4x)]dx/4
=x/4-sin(4x)/16+C
(其中C为任意常数)