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CBSE Class 12-science Answered

Integrate the following functions w.r.t.x.
 
1) sec^n x. tanx
 
2)  cosx
     1-sinx
Asked by aadeshpdabre | 05 Apr, 2016, 08:41: PM
answered-by-expert Expert Answer
1. space integral sec to the power of straight n straight x. tanx space dx space equals space integral sec to the power of straight n minus 1 end exponent straight x. secxtanx space dx Put space secx space equals space straight t rightwards double arrow straight d left parenthesis secx right parenthesis space equals space dt rightwards double arrow secx. space tanx space dx space equals space dt rightwards double arrow dx space equals space dt over secxtanx Putting space space secx space equals space straight t space and space dx space equals space dt over secxtanx space in space the space integral comma space we space get integral sec to the power of straight n minus 1 end exponent straight x. secxtanx space dx equals integral straight t to the power of straight n minus 1 end exponent space dt space space equals space straight t to the power of straight n over straight n plus straight c space equals space fraction numerator sec to the power of straight n straight x over denominator straight n end fraction plus straight c space 2. space integral fraction numerator cosx over denominator 1 minus sinx end fraction dx Put space straight t space equals space 1 space minus space sinx rightwards double arrow dt space equals space space minus cosx space dx integral fraction numerator cosx over denominator 1 minus sinx end fraction dx space equals space integral fraction numerator negative dt over denominator straight t end fraction space equals space minus log open vertical bar straight t close vertical bar space plus space straight C space equals space minus log open vertical bar 1 minus sinx close vertical bar space plus space straight C space
Answered by Rebecca Fernandes | 06 Apr, 2016, 09:26: AM

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