Show that: `int_a^bf(x)dx=int_(a+c)^(b+c)f(x-c)dx` and hence show that `int_0^pi sin^100xcos^99xdx=0`

int_0^(2pi)sin^(100)xcos^(99)x dx

int_0^(pi) sin^(50)x.cos^(49)xdx=

Show that int_(0)^( pi) co s^(99) x dx =0

Let int_(a)^(b)f(x)dx=int_(a+c)^(b+c)f(x-c)dx . Then the value of int_(0)^(pi)sin^(2010)x*cos^(2009)xdx is

int_(0)^(pi)(sin2xcos3x)dx=?

Prove that int_a^bf(x)dx=int_(a+c)^(b+c)f(x-c)dx , and when f(x) is odd function, int_(-a)^af(x)dx=0

Prove that int_a^bf(x)dx=int_(a+c)^(b+c)f(x-c)dx , and when f(x) is odd function, int_(-a)^af(x)dx=0

Evaluate int_(0)^(2pi)sin^(100)xcos^(99)xdx .

Prove that int_0^a f(x)dx=int_0^af(a-x)dx , hence evaluate int_0^pi(x sin x)/(1+cos^2 x)dx