(I)
The process of differentiation and integration are inverses of each other in the
sense of the following results :
( )
d
f x dx
dx ∫
 = f (x)
and
f( )
∫′x dx
 = f (x) + C, where C is any arbitrary constant Fig 7 1
INTEGRALS         293
Proof Let F be any anti derivative of f, i e