`int_0^(pi//2)(theta/sintheta)^2d theta=`

int_0^(pi/2) d theta

If int_0^a(dx)/(sqrt(x+a)+sqrt(x))=int_0^(pi/8)(2tantheta)/(sin2theta)d theta then value of ' a ' is a equal to (a >0) (a) 3/4 (b) pi/4 (c) (3pi)/4 (d) 9/(16)

Iflambda=int_0^(pi/2)costhetaf(sintheta+cos^2theta)dtheta a n dI_2=int_0^(pi//2)sin2thetaf(sintheta+cos^2theta)dtheta,t h e n I_1=-2I_2 (b) I_1=I_2 2I_1=I_2 (d) I_1=-I_2

Evaluate: int_0^(pi//2)(costheta)/((1+sintheta)(2+sintheta)) d theta

Evaluate: int_0^(pi//2)sqrt(costheta)sin^3theta d theta

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)d theta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin theta d theta =-pilog2.

If f(x)=1/pi int_0^(pi/2) sin^2(ntheta)/sin^2theta d(theta) then evaluate (f(15)+f(3))/(f(15)-f(9))

9. int_0^(pi/2)sec^4theta d theta