∫√(8-x^2)dx,可知-√8≤x≤√8
设x=√8sint,则t=arcsin(x/√8)
√(8-x^2)=√{8[1-(sint)^2]}=√8*cost
dx=√8costdt
∴∫√(8-x^2)dx
=∫√8*cost*√8costdt
=8∫(cost)^2dt
=8∫[(1+cos2t)/2]dt
=4t+2sin2t+C
[其中,t=arcsin(x/√8)]
∫√(8-x^2)dx,可知-√8≤x≤√8
设x=√8sint,则t=arcsin(x/√8)
√(8-x^2)=√{8[1-(sint)^2]}=√8*cost
dx=√8costdt
∴∫√(8-x^2)dx
=∫√8*cost*√8costdt
=8∫(cost)^2dt
=8∫[(1+cos2t)/2]dt
=4t+2sin2t+C
[其中,t=arcsin(x/√8)]