`1/(piln2)int_(pi/2)^0lnsin2x dx=`

int_(0)^(1) lnsin(pi/2x) dx

int_(0)^(1) lnsin(pi/2x) dx

Evaluate int_(0)^(pi//2)lnsin2xdx

Evaluate int_(0)^(pi//2)lnsin2xdx

Statement-1: int_(0)^(pi//2) x cot x dx=(pi)/(2)log2 Statement-2: int_(0)^(pi//2) log sin x dx=-(pi)/(2)log2

Evaluate the following integrals (i) int_(R)^(oo)(GMm)/(x^(2))dx (ii) int_(r_(1))^(r_(2))-k(q_(1)q_(2))/(x^(2))dx (iii) int_(u)^(v)Mvdv (iv) int_(0)^(oo)x^(-1//2)dx (v) int_(0)^(pi//2)sin x dx (vi) int_(0)^(pi//2)cos x dx (vii) int_(-pi//2)^(pi//2) cos x dx

Show that (a) int_(0)^(pi/2) sin x dx=1 (b) int_(0)^(pi) cosx dx=0

The value of int_(0)^(2) 3x^(2)dx+int_(0)^(pi//2) sin x dx is :-