Using `int_a^bf(a+b-x)dx=int_a^bf(x)` prove the following :

STATEMENT 1 : The value of int_0^1tan^(-1)((2x-1)/(1+x-x^2)) dx=0 STATEMENT 2 : int_a^bf(x)dx=int_0^bf(a+b-x)dx then Which of the following statement is correct ?

STATEMENT 1 : The value of int_0^1tan^(-1)((2x-1)/(1+x-x^2)) dx=0 STATEMENT 2 : int_a^bf(x)dx=int_0^bf(a+b-x)dx then Which of the following statement is correct ?

int_a^b logx/x dx

int_a^b[d/dx(f(x))]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

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

Statement I int_0 ^ (npi + t) | sinx | dx = (2n + 1) -cost, (0 leq t leq pi) Statement II int_a ^ bf (x) dx = int_a ^ ef (x) dx + int_e ^ bf (x) dxint_0 ^ (na) f (x) dx = nint_0 ^ af (x) dx "if" f (a + x) = f (x)

STATEMENT 1: int_0^pisin^(100)xcos^(99)xdx is z ero . 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

Statement 1: The value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to pi/6 Statement 2: int_a^bf(x)dx=int_a^bf(a+b-x)dxdot Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true