⑩串紫学 Teaching Plan on Advanced Mathematics 例9求x3√4-x g C 解:令x=2 sint dx=2 cos tdt t∈ 22 ∫x2√4-x2=」(2siny、4-4sm2t2ct 32 sin tcos'tdt =32 sint(1-cos?t)cos'tdt =-32∫cos2t- cost)d cost -320coSt--coSt)+C √4-x2J+ x+C xTianjin Polytechnic University Teaching Plan on Advanced Mathematics 例9 求 4 . 3 2 x x dx  − 令 x = 2sint dx = 2costdt          − 2 , 2 t x x dx  − 3 2 4 (2sint) 4 4sin t 2costdt 3 2 = −   t tdt 3 2 32 sin cos =  t t tdt 2 2 32 sin (1 cos )cos =  − 32 (cos t cos t)d cost 2 4 = −  − = − t − cos t) + C 5 1 cos 3 1 32( 3 5 t 2 x 2 4 − x ( ) ( 4 ) . 5 1 4 3 4 5 2 3 2 = − − x + − x + C 解：