`int _(0)^(pi/2)sinxdx`

Evaluate the following integrals (i) int_(R)^(oo)(GMm)/(x^(2))dx (ii) int_(r_(1))^(r_(2)) -k(q_1q_2)/(x^(2))dx (iii) int_(u)^(v) Mv dv (iv) int_(0)^(oo) x^(-1//2) dx (v) int_(0)^(pi//2) sinx dx (vi) int_(0)^(pi//2) cosx dx (vii) int_(-pi//2)^(pi//2) cos x dx

Evaluate the integral as limit of sum: int_(0)^(pi)sinxdx

Evaluate : int_0^(pi/2)x^2sinxdx

Evaluate: int_0^(pi//2)sinx\ dx

Evaluate : int_0^(pi//2)sinx\ dx

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

Show that (i) int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x (ii) int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x (iii) int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x

I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then

Consider the definite integrals A=int_(0)^(pi)sinx cosx^(2)xdx and B=int_(0)^((pi)/(2))sinx cos^(2)xdx . Then,

The value of int_(0)^(pi//2)logsinxdx is equal to