b a  x b Second definition of the definite Integral a x b If f(x) is continuous in the interval we definite the area enclosed by the y = f(x), the ordinates x = a, x = b, and the x axis as the definite integral of b ( f x)dx a 7.4 Some important properties of definite Integral: If f(x) is continuous in a 1. ( ) 0 f x dx  a b a )dx (  f x f x 2.  x b and c is a point between a and b a b a 3. If f is integrable in b c b ( )dx ( ) ( )dx   f x f x dx f x a a c a  x b 4. If f(x) is integrable in and c is any constant then  b b c ( )  ( )dx f x dx f x c  a a c b  a a  x b 5. If f(x) is integrable in and m is any constant then 64 b mb ( )dx  f x f m dx ma b b m a a m
b a x b  Second definition of the definite Integral If f(x) is continuous in the interval a x b we definite the area enclosed by the y = f(x), the ordinates x = a, x = b, and the x axis as the definite integral of b f ( x)dx a 7.4 Some important properties of definite Integral: If f(x) is continuous in 1. a a f ( x ) dx  0 b a 2. f x )dx  f ( x a b 3. If f is integrable in a x b  and c is a point between a and b b c b f ( x )dx  f ( x ) dx  f ( x )dx a a c 4. If f(x) is integrable in a x b  and c is any constant then b b  c f ( x ) dx  f ( x c )dx a a  c b  a 5. If f(x) is integrable in a x b  and m is any constant then 64 b mb f ( x )dx  ma f m dx b b m a a m
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