InterviewSolution
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InterviewSolution
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What is the value of `int(dx)/((x^(2) + a^(2)) (x^(2) + b^(2)))` ?A. `int([{tan^(-1) (x//a)}//a - {tan^(-1) (x//b)}//b])/((a^(2) + b^(2))) + c`B. `int([{tan^(-1) (x//a)}//a + {tan^(-1) (x//b)}//b])/((a^(2) +b^(2))) + c`C. `int([{tan^(-1) (x//a)}//a + {tan^(-1)(x//b)}//b])/((b^(2) -a^(2))) + c`D. `int([{tan^(-1) (x//a)} //a+ {tan^(-1) (x //b)}//b])/((b^(2) - a^(2))) + c` |
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Answer» Correct Answer - D The given integral is `int (dx)/((x^(2) + a^(2)) (x^(2) + b^(2)))` Breaking the expression under integral into partial fraction `(1)/((x^(2) + a^(2)) (x^(2) + b^(2)))` `= ((1)/((x^(2) + a^(2))) - (1)/((x^(2) + b^(2)))) xx (1)/(b^(2) -a^(2))` The given integral is `(1)/((b^(2) -a^(2))) int ((1)/((x^(2) + a^(2))) - (1)/((x^(2) + b^(2))))dx` `= (1)/((b^(2) -a^(2))) int [(1)/(x^(2) + a^(2)) dx - int (1)/(x^(2) + b^(2)) dx]` `= (1)/((b^(2) -a^(2))) {(tan^(-1) ((x)/(a)))/(a) - (tan^(-1) ((x)/(b)))/(b)} + c` |
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