13. Leibnitz Rule for Differentiation Under Integral Sign
( a) If Φ( x) and ψ( x) are defined on [ a, b ] and differentiable for every x and f( t) is continuous, then
( b) If Φ( x) and ψ( x) are defined on [ a, b ] and differentiable for every x and f( t) is continuous, then
14. If f( x) ≥ 0 on the interval [ a, b ], then 15. If( x) ≤ Φ( x) for x ∈ [ a, b ], then
16. If at every point x of an interval [ a, b ] the inequalities
g( x) ≤ f( x) ≤ h( x) are fulfilled then,
18. If m is the least value and M is the greatest value of the function f( x) on the interval [ a, bl.( estimation of an integral), then
19. If f is continuous on [ a, b ], then there exists a number c in [ a, b ] at which
is called the mean value of the function f( x) on the interval [ a, b ].