Question

数学题.哪个数的导数是根号下1-x² ?谢谢.快

Answer 1

∫√1-x² dx

x=sint

cost=√1-x²

sin2t=2x√1-x²

dx=costdt

∫√1-x² dx

=∫costcostdt

=∫cos²tdt

=∫(1+cos2t)/2dt

=1/2(t+1/2∫cos2td2t)+C

=t/2+1/4sin2t+C

=1/2arcsinx+1/2x√1-x²+C