InterviewSolution
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InterviewSolution
| 1. |
`int_0^pi[cotx]dx`, where [.] denotes the greatest integerfunction, is equal to(1) `pi//2`(2) 1(3) `1`(4) `pi//2` |
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Answer» `I = int_0^pi [ cot x] dx` `= int_0^pi [ cot(pi- x)] dx` `= int_0^pi [cot(pi-x)] dx` `= int _0^ pi [ - cot x] dx` `(i) + (ii)` `2 I= int_0^pi [ cot x] + int_0^pi [-cot x] dx` `[x] + [-x] = -1 x !in z` `= 0 x !in z` `2I= int_0^pi -1 dx` `2I = -1 xx pi ` `I = - pi/2` option 4 is correct |
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