If `int(sec^(2)x-2010)/(sin^(2010)x)dx=(P(x))/(sin^(2010) x)+C`, then value of `P((pi)/(3))` is

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)

If int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=In2, then the value of int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to:

If the product of all solutions of the equation ((100)x)/(2010)=(2009)^(log_(x)(2010)) form as (m)/(n) then the value of (m-n) is

If f'(x)=(x-a)^(2010)(x-b)^(2009) and agtb , then

If f'(x)=(x-a)^(2010)(x-b)^(2009) and agtb , then

If f'(x)=(x-a)^(2010)(x-b)^(2009) and agtb , then

The value of int_(0)^(pi) x sin^(3) x dx is