how to integrate the function using substitution method ?

Asked by NAKSHATRA | 4th Nov, 2014, 09:01: AM

Expert Answer:

I n t e g r a l s space o f space c e r t a i n space f u n c t i o n s space c a n n o r space b w space o b t a i n e d space d i r e c t l y. space I f space t h e y space a r e space n o t space i n space space s tan d a r d space f o r m comma space t h e y space m a y space b e space r e d u c e d space t o space s tan d a r d space f o r m s space b y space s u b s t i t u t i o n. T h i s space m e t h o d space o f space e v a l u a t i n g space b y space a space p r o p e r space s u b s t i t u t i o n space i s space c a l l e d space i n t e g r a t i o n space b y space s u b s t i t u t i o n. I f space g open parentheses x close parentheses space i s space a space c o n t i n u o u s space d i f f e r e n t i a b l e space f u n c t i o n comma space t h e n space t o space e v a l u a t e space i n t e g r a l s space o f space t h e space f o r m integral f open parentheses g open parentheses x close parentheses close parentheses cross times g apostrophe open parentheses x close parentheses d x w e space s u b s t i t u t e comma space g open parentheses x close parentheses equals t space a n d space g apostrophe open parentheses x close parentheses d x equals d t T h u s comma space s u b s t i t u t i o n space r e d u c e s space t h e space a b o v e space i n t e g r a l space t o space integral f open parentheses t close parentheses d t. A f t e r space e v a l u a t i n g space t h e space i n t e g r a l comma space integral f open parentheses t close parentheses d t comma space w e space s u b s t i t u t e space b a c k space t h e space v a l u e space o f space t.

Answered by Vimala Ramamurthy | 4th Nov, 2014, 11:12: AM