1,int sin(2x+(pi)/(2))dx

int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

If x in(-pi,pi) then int sqrt(1+sin((x)/(2)))dx

1) int_(-(pi)/(2))^(pi)sin^(-1)(sin x)dx 2) int_(-(pi)/(2))^((pi)/(2))(-(pi)/(2))/(sqrt(cos x sin^(2)x))dx 3) int_(0)^(2)2x[x]dx

int_(-pi)^( pi)(sin^(2)x)/(1+a^(x))dx

(i) Show that int_(0)^(pi)xf(sinx)dx =(pi)/(2)int_(0)^(pi)f (sin x)dx. (ii) Find the value of int_(-1)^(3//2)|x sin pix|dx .

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

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