If a function f (x) is continuous in a closed interval [a, b] i.e.
a â‰¤ x â‰¤ b, and derivable in open interval (a, b) i.e. a < x < b, and if f (a) = f (b), then there exist atleast one real c in (a, b) such that f â€²(c) = 0
Lagrangeâ€™s first mean value theorem
If a function f (x) is continuous in closed interval [a, b] and fâ€™(x) exist in open interval (a, b) then there exist atleast one value of c such that,
f â€²(c)
Standard Integration
; (a = constant)
when n = 1, i.e.,
u is first function, v is second function. To find first function out of two we follow â€˜ILATEâ€™ rule.