解答题
17.设y'=arctan(x一1)2，y(0)=0，求∫01y(x)dx．
【正确答案】∫01y(x)dx=xy(x)|01-∫01xarctan(x一1)2dx
=y(1)一∫01(x一1)arctan(x一1)2d(x一1)一∫01arctan(x一1)2dx
=y(1)一∫01(x一1)arctan(x一1)2d(x一1)一∫01arctan(x一1)2dx
【答案解析】