InterviewSolution
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InterviewSolution
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`intsqrt(1-4x-x^(2))dx`A. `(x)/(2)sqrt(1-4x-x^(2))+(5)/(2)sin^(-1)((x+2)/(sqrt5))+C`B. `(x)/(2)sin^(-1)((x+2)/(sqrt5))+(5)/(2)sqrt(1-4x-x^(2))+C`C. `(x+2)/(2)sin^(-1)((x+2)/(sqrt5))+(5)/(2)sqrt(1-4x-x^(2))+C`D. `(x+2)/(2)sqrt(1-4x-x^(2))+(5)/(2)sin^(-1)((x+2)/(sqrt5))+C` |
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Answer» Correct Answer - D Let `l=intsqrt(1-4x-x^(2))dx` `=intsqrt(-(x^(2)+4x-1-2^(2)+2^(2)))dx` `=int sqrt(-[(x+2)^(2)-(sqrt5)^(2)])dx` `=intsqrt((sqrt5)^(2)-(x+2)^(2))dx` `[because int sqrt(a^(2)-x^(2))dx=(x)/(2)sqrt(A^(2)-x^(2))+(a^(2))/(2)sin^(-1).(x)/(a)+C]` `rArr " "l=(x+2)/(2)sqrt(1-4x-x^(2))+(5)/(2)sin^(-1).((x+2))/(sqrt5)+C` |
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