InterviewSolution
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InterviewSolution
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फलन `int(dx)/(sqrt(2+x-3x^(2)))` का x के सापेक्ष समाकलन कीजिए । |
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Answer» माना `I=int(dx)/(sqrt(2+x-3x^(2)))=int(dx)/(sqrt(2-3(x^(2)-(x)/(2)))` `=int(dx)/(sqrt(2-3{x^(2)-(x)/(3)+(1)/(36)-(1)/(36)})" "` (पूर्ण वर्ग बनाने पर ) `=int(dx)/(sqrt(2+(1)/(12)-3(x-(1)/(6))^(2))=(1)/(sqrt3)int(dx)/(sqrt(((5)/(6))^(2)-(x-(1)/(6))^(2)))` माना `x-(1)/(6)=t therefore dx = dt` तथा `(5)/(6)=a` `therefore" "I=(1)/(sqrt3)int(dt)/(sqrt(a^(2)-t^(2)))=(1)/(sqrt3)sin^(-1)((t)/(a))` `=(1)/(sqrt3)sin^(-1){(x-(1)/(6))/((5)/(6))}=(1)/(sqrt3)sin^(-1)[(6x-1)/(5)]` |
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