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CBSE Class 12-science Answered

Evaluate integral fraction numerator 1 d x over denominator x left parenthesis x to the power of 10 minus 7 right parenthesis end fraction
Asked by Eng.surinder.singh | 25 Jan, 2019, 12:39: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator dx over denominator straight x open parentheses straight x to the power of 10 minus 1 close parentheses end fraction
straight I equals integral fraction numerator straight x to the power of 9 dx over denominator straight x to the power of 10 open parentheses straight x to the power of 10 minus 1 close parentheses end fraction
Put space straight x to the power of 10 equals straight t
10 straight x to the power of 9 dx equals dt
straight x to the power of 9 dx equals dt over 10
straight I equals integral fraction numerator begin display style dt over 10 end style over denominator straight t open parentheses straight t minus 1 close parentheses end fraction
straight I equals 1 over 10 integral fraction numerator dt over denominator straight t squared plus straight t end fraction
straight I equals 1 over 10 integral fraction numerator dt over denominator straight t squared plus straight t plus begin display style 1 fourth end style minus begin display style 1 fourth end style end fraction
straight I equals 1 over 10 integral fraction numerator dt over denominator open parentheses straight t plus begin display style 1 half end style close parentheses squared minus open parentheses begin display style 1 half end style close parentheses squared end fraction
Using space integral fraction numerator dx over denominator straight x squared minus straight a squared end fraction space formula space integrate space it space further.
end style
Answered by Sneha shidid | 25 Jan, 2019, 04:46: PM
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