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

STATEMENT 1: The value of int_0^(2pi)cos^(99)x dxi s0 STATEMENT 2: int_0^(2a)f(x)dx=2int_0^af(x)dx ,iff(2a-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

Evaluate: int_0^1 xsqrt(1+x^2) dx

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

Evaluate: int_0^1 2xsqrt(1+x^2) dx

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)dtheta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin"thetadtheta"=-pilog2.

Evaluate: int_0^1 e^(2-3x) dx

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(x) is an odd function.