XII Maths Chapter 8. Application of Integrals | Page 5

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 .