InterviewSolution
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InterviewSolution
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`int1/(sqrt(8+3x-n^2))dx`A. `(2)/(3)sin^(-1)((2x-1)/(sqrt(41)))+C`B. `(3)/(2)sin^(-1)((2x-3)/(sqrt(41)))+C`C. `(1)/(sqrt(41))sin^(-1)((2x-3)/(sqrt(41)))+C`D. `sin^(-1)((2x-3)/(sqrt(41)))+C` |
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Answer» Correct Answer - D Let `I=int(1)/(sqrt(8+3x-x^(2)))dx` `=int(1)/(sqrt(8-[x^(2)-3x+((3)/(2))^(2)-((3)/(2))^(2)]))dx` `=int(1)/(sqrt(8-[(x-(3)/(2))^(2)-(9)/(4)]))dx` `=int(1)/(sqrt(8+(9)/(4)-(x-(3)/(2))^(2)))dx` `=int(1)/(sqrt(((sqrt(41))/(2))^(2)-(x-(3)/(2))^(2)))dx` Let `x-(3)/(2)=t rArr dx=dt` `therefore" "I=int(1)/(sqrt(((sqrt(41))/2)^(2)-t^(2)))dt=sin^(-1)((t)/((sqrt(41))/(2)))+C` `=sin^(-1)((2x-3)/(sqrt(41)))+C` |
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