STATEMENT 1: The value of `int_0^(2pi)cos^(99)x dx` is 0 STATEMENT 2: `int_0^(2a)f(x)dx=2int_0^af(x)dx` ,if `f(2a-x)=f(x)` which of the statement is correct?Is statement 2 correct explanation of statement 1?

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 ?

The value of int_0^(pi/2)dx/(1+tan^3x) is

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

STATEMENT 1: int_0^pixsinxcos^2xdx=pi/2int_0^pisinxcos^2x dx . STATEMENT 2: int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx .

STATEMENT 1: int_0^pisqrt(1-sin^2x) dx=0 , STATEMENT 2: int_0^picosx dx=0

int_(0)^(2a)(f(x)dx)/(f(x)+f(2a-x))=a

Evalute: int_0^(pi)(xsinx)/(1+cos^2x)dx .

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)d theta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin theta d theta =-pilog2. (a) statement 1 is true, statement 2 is true, Statement 2 is the correct explanation for statement 1. (b) statement 1 is true, statement 2 is true, Statement 2 is not correct explanation for statement 1. (c) statement 1 is true, statement 2 is not true. (d) statement 2 is true, statement 1 is not true.

STATEMENT 1 : The value of int_(-4)^(-5)sin(x^2-3)dx+int_(-2)^(-1)sin(x^2+12 x+33) is zero. STATEMENT 2 : int_(-a)^af(x)dx=0iff f(x) is an odd function.

'If int_(1)^(2)f(x)dx=int_(1)^(2)g(x)dx , then f(x)=g(x) ''. Examine the validity of the statement with examples.