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Let f(x)=[3+4 sin x] (where [ ] denotes ...

Let `f(x)=[3+4 sin x]` (where [ ] denotes the greater integer function). If sum of all the values of 'x' in `[pi,2pi]` where f(x) fails to be differentiable is `(k pi)/2`, then find the value of k.

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`f(x) = (3 + 4sin x)`
`=> pi, pi + theta, pi + pi/6 , pi+ phi, (3 pi)/2 + phi, 2pi - pi/6 , 2 pi - theta , 2 pi`
now, `3 + 4 sin x = 1`
`sin x = -2/4 = -1/2`
so, `pi + pi + theta + pi + pi/6 + 3 pi/2 - phi + 3 pi/2 + phi + 2pi - pi/6 + 2 pi - phi + 2 pi = k pi/2`
`=> 12 pi= k pi/2 `
`k= 24`
Answer
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