 # Doubt from Integration

Q 16 and 17
In Q 17 can we consider [x] as odd function as it's graph is symmetric about origin

Q12

I have derived it's reduction formula but can't transform it into this form.

Go with beta function these r application of beta function

#15 Its king and add property ans will be 9

No its neither odd nor even
[x]+[-x]= -1 piece wise defined function it may be zero also

#16 try to make perfect square then u will the results

So, what's your approach for Q 17

Same even odd property take common u will get result i mean king property
Zero ans?

Yes

Don't know where I am wrong, may be some silly mistake?

see a=0 directly satisfies the inequalitiy....
Now the take given integrand as f(x) now clearly a<0 and the integration will be less than zero only amd only if graph of f(x) is below x axis ...

Now f(0) = -1 and f(-1) is 63 and f'(x) <0 for x <0 hence monotonic
therefore f(x) is zero for some m E(-1,0) and f(x) will be above y axis for values less than m .....therefore there is no otjer integral value of a to satisfy the inequality ......
hence ans is (B) 1

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