求∫1-1[x+√(1-x2)2]dx．

求∫1-1[x+√(1-x2)2]dx．
【正确答案】：∫1-1[x+√(1-x2)2]dx =∫1-1[x2+2x√(1-x2)+1-x2]dx =∫1-1dx-∫1-1[√(1-x2)]d(1-x2) =x∣1-1-(2/3)(1-x2)3/2∣1-1=2