int_(0)^( pi/2)((pi)/(2)-x)sec xdx" is equal to "

int_(0)^(pi//2) e^(sin)x cos xdx is equal to

int_(0)^( pi/2)sec^(2)xdx

int_(0)^( pi/2)sec^(2)xdx

int_(0)^((pi)/(4))sec xdx

int_((pi)/(4))^((pi)/(3))sec^(2)xdx

int_(0)^( pi/2)e^(x)xdx=

The value of lim_(x rarr oo)(int_(0)^((pi)/(2))sin^(2m)xdx)/(int_(0)^((pi)/(2))sin^(2m+1)xdx) is equal to

int_(0)^( pi/2)x sec^(2)xdx

int_(0)^( pi/2)x^(2)cos^(2)xdx