STATEMENT 1: `int_0^pisin^(100)xcos^(99)xdxi sz e rodot` STATEMENT 2: `int_a^bf(x)dx=int_(a+c)^(b+c)f(x-c)dx ,a n d` for odd function, `int_(-a)^af(x)dx=0`

Answer

`0`

Explanation

`I=int_(0)^(2pi)sin^(100)xcos^(99)x dx`
Here `f(x)=sin^(100)x cos^(99) x` for which `f(2pi-x)=f(x)`
`:.I=2int_(0)^(pi)sin^(100)xcos^(99)xdx`
`=2int_(0)^(pi)sin^(100)(pi-x)cos^(99)(pi-x)dx`
`=-2int_(0)^(pi)sin^(100)xcos^(99)xdx`
`=-I`
or `2I=` or `I=0`