568] 
NOTE ON THE INTEGRALS 
cos x~ dx and I sin x~ dx. 
63 
which is independent of b, say this is 
_ G_ 
U ~ vW’ 
and thence differentiating in regard to b, we find 
du _ 1 
db~~Yb U ’ 
the theorem in question. 
But the value of ^ cannot be obtained by differentiating under the integral sign, 
for this would give 
and this integral is certainly indeterminate.