" 5."int_(0)^( pi)lcos x1dx

int_(0)^(2 pi)cos^(5)x*dx

int_(0)^(pi) cos^(5) x dx=

Evaluate: int_(0)^(1)|5x-3|dx( ii) int_(0)^( pi)|cos x|dx( iii) int_(-5)^(5)|x-2|dx( iv )int_(-1)^(1)e^(|x|)dx(v)int_(0)^(2)|x^(2)+2x-3|dx(v)int_(1)^(4)(|x-1|+|x-2|+|x-3|)dx( vi) int_(1)^(2)|x^(3)-x|dx

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

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

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

If A=int_(0)^( pi)(cos x)/((x+2)^(2))dx, then int_(0)^( pi/2)(sin2x)/(x+1)dx is equal to

Prove that: int_(0)^(pi)cos^(5)x dx = 0