`f (x) =a cos (piy)+b, f'((1)/(2))=pi and int _(1//2)^(3//2) f (x) dx =2/pi+1,` then find the value of `-(12)/(pi) ((sin ^(-1) a )/(3) + cos ^(-1)b ).`

If f(x)=x+sin x, then find the value of int_(pi)^(2 pi)f^(-1)(x)dx

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

Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

Find the value of int_(pi/4)^(pi/3) (sin2x)/(1-cos2x) dx

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

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

If f(x)=3+cos^-1(cos(pi/2+x)cos(pi/2-x)+sin(pi/2+x)sin(pi/2-x)) , x in [0,pi] then find the minimum value of f(x) is