设I=∫﹙a+x)/根号下(a²-x²)dx 则I=?求详解

问题描述:

设I=∫﹙a+x)/根号下(a²-x²)dx 则I=?求详解

I=∫﹙a+x)/根号下(a²-x²)dx 令x=asint,则dx=acostdt
=∫﹙a+asint)/(acost)*acostdt
=∫﹙a+asint)dt
=at-acost+C
=a*arcsin(x/a)-√(a²-x²) +C