20. If f 2 2( x) and g 2( x) are integrable on [ a, b ], then
21. Let a function f( x, α) be continuous for a ≤ x ≤ b and c ≤ α ≤ d. Then, for any α ∈ [ c, d ], if
22. If f( t) is an odd function, then is an even function.
23. If f( t) is an even function, then is an odd function.
24. If f( t) is an even function, then for non-zero a, is not necessarily an odd function. It will be an odd function, if
25. If f( x) is continuous on [ a, α ], then is called an improper integral and is defined as
27. Geometrically, for f( x) > 0, the improper integral gives area of the figure bounded by the curve y = f( x), the axis and the straight line x = a.
Integral Function
Let f( x) be a continuous function defined on [ a, b ], then a function φ( x) defined
by is called the integral function of the function f.