InterviewSolution
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InterviewSolution
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फलन `intsqrt((5+4x-x^(2))dx` का x के सापेक्ष समाकलन कीजिए । |
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Answer» माना `I=intsqrt((5+4x-x^(2)))dx` `=intsqrt(5-(x^(2)-4x+4-4))dx" "` (पूर्ण वर्ग बनाने पर ) `=intsqrt(9-(x-2)^(2))dx=intsqrt((3)^(2)-(x-2)^(2))dx` माना `3=a` तथा `x-2=t therefore dx=dt` `therefore I=intsqrt((a^(2)-t^(2)))dx=(t)/(2)sqrt((a^(2)-t^(2)))+(1)/(2)sqrt(a^(2)-t^(2))+(1)/(2)a^(2)sin^(-1)((t)/(a))` `=((x-2)/(2))sqrt(9-(x-2)^(2))+(1)/(2)(3)^(2)sin^(-1)((x-2)/(3))` `=(1)/(2)(x-2)sqrt(5+4x-x^(2))+(9)/(2)sin^(-1)((x-2)/(3))` |
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