int_(-1)^(1/2)|x cos(pi x)|dx

int_(-1)^(1/2)|x cos(pi x)|backslash dx

int_(0)^(pi/2)(x)/(1+cos x)dx =

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

If I_(1)=int_(0)^(pi//2)"x.sin x dx" and I_(2)=int_(0)^(pi//2)"x.cos x dx" , then

If int_(0)^(pi//2) ln (sin x) dx= - pi/2 ln 2 then int_(0)^(pi) ln (1+ cos x) dx=

int_(0)^(pi//2) (sin x cos x) / ((1 + 2 sin x ) ( 1+ sin x))dx =

int_(0)^(pi//2)(1)/(2+cos x)dx=