Let `f(x)=int dx/((x^2+1)(x^2+9))` and `f(0)=0`, if `f(sqrt3)=(5/36)k`, then k is
a) `pi/6`
b)`pi/3`
c) `pi/2`
d) `pi/4`

f(x)=sin+sqrt(3)cosx is maximum when x= pi/3 (b) pi/4 (c) pi/6 (d) 0

IF f(x)=A si n ((pi x)/2)+B and f'(1/2)=sqrt2 and int_0^1 f(x)dx =(2A)/pi then what is the value of B

Let F(x)=int e^(sin^(-1)x)(1-(x)/(sqrt(1-x^(2))))dx and F(0)=1, If F((1)/(2))=(k sqrt(3)e^((pi)/(6)))/(pi), then the value of k is

If I_(1)=int_(3pi)^(0) f(cos^(2)x)dx and I_(2)=int_(pi)^(0) f(cos^(2)x) then

If P = int_(0)^(3pi) f(cos^(2)x)dx and Q=int_(0)^(pi) f(cos^(2)x)dx , then

For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4 (c) (3pi)/4 (d) (4pi)/3

If f(x)=A sin((pi x)/(2))+b,f'((1)/(2))=sqrt(2) and int_(0)^(1)f(x)dx=(2A)/(pi), then constants A and B are (pi)/(2)and(pi)/(2) (b) (2)/(pi) and (3)/(pi)0 and -(4)/(pi) (d) (4)/(pi) and 0

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

If f'(x)=k(cos x-sin x),f'(0)=3 and f((pi)/(2)) find f'(x)