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Evaluate and please show workings. 10 points to the best answer.?

0 votes
∫log tdt
     e
asked Apr 24, 2013 in CALCULUS by Jose Rodriguez Rookie

1 Answer

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integral italic log subscript e t d t equal integral italic log subscript e t cross times 1 d t    (integral f open parentheses x close parentheses g open parentheses x close parentheses d x equal f open parentheses x close parentheses integral g open parentheses x close parentheses d x minus integral open parentheses d open parentheses f open parentheses x close parentheses close parentheses integral g open parentheses x close parentheses d x close parentheses d x right parenthesis

space space space space space space space space space space space space space space space space equal italic log subscript e t cross times integral 1 d t minus integral open parentheses 1 over t integral 1 d t close parentheses d t   

space space space space space space space space space space space space space space space space equal italic log subscript e t cross times t minus integral open parentheses 1 over t t close parentheses d t   (Inverse of derivative is equal to integration)

space space space space space space space space space space space space space space space space equal t italic log subscript e t minus integral 1 d t

space space space space space space space space space space space space space space space space equal t italic log subscript e t minus t

space space space space space space space space space space space space space space space space equal t open parentheses italic log subscript e t minus 1 close parentheses

space space space space space space space space space space space space space space space space equal t open parentheses italic log subscript e t minus italic log subscript e e close parentheses

space space space space space space space space space space space space space space space space equal t open parentheses italic log subscript e t over e close parentheses                  (Apply logarithms formula italic log subscript e open parentheses a over b close parentheses equal italic log subscript e open parentheses a close parentheses minus italic log subscript e open parentheses b close parentheses)

 

answered Apr 24, 2013 by diane Scholar

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