`Iff(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d` `int_0^1f(x)dx=(2A)/pi,t h e ncon s t a n t sAa n dBa r e` `pi/2a n dpi/2` (b) `2/pia n d3/pi` `0a n d-4/pi` (d) `4/pia n d0`

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

If f(x)=sinx ,AAx in [0,pi/2],f(x)+f(pi-x)=2,AAx in (pi/2,pi)a n df(x)=f(2pi-x),AAx in (pi,2pi), then the area enclosed by y=f(x) and the x-axis is pis qdotu n i t s (b) 2pis qdotu n i t s 2s qdotu n i t s (d) 4s qdotu n i t s

If f(1)=3,f^(prime)(1)=2,f^(1)=4,t h e n(f^(-1))^()(3)= a. 1 b. -1/2 c. -2 d. none of these

If int_0^(pi^2/4) (2sinsqrt(x)+sqrt(x)cossqrt(x))dx=pi^2/n , then n = ….

If I_n=int_0^(pi/2) x^n sinx dx , then [I_4+12I_2] is equal to (A) 4pi (B) 3(pi/2)^3 (C) (pi/2)^2 (D) 4(pi/2)^3

If f (n)= 1/pi int _(0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2) theta), n in N, then evulate (f (15)+ f (3))/( f (12) -f (10)).

A general solution of tan^(2)theta+cos2 theta=1 is (n in Z)n pi=(pi)/(4) (b) 2n pi+(pi)/(4)n pi+(pi)/(4) (d) n pi

The function f(x)=tan x is discontinuous on the set {n pi;n in Z}{(2n+1)(pi)/(2):n in Z}(d){(n pi)/(2):n in Z}