`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)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int_0^1f(x)dx=(2A)/pi the constants A and B are (a) pi/2a n dpi/2 (b) 2/pia n d3/pi (c) 0a n d-4/pi (d) 4/pia n d0

If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int_0^1f(x)dx=(2A)/pi the constants A and B are (a) pi/2a n dpi/2 (b) 2/pia n d3/pi (c) 0a n d-4/pi (d) 4/pia n d0

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If I_1=int_0^pixf(sin^3x+cos^2x)dxa n d I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx ,t h e nr e l a t eI_1a n dI_2

If I_1=int_0^pixf(sin^3x+cos^2x)dxa n d I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx ,t h e nr e l a t eI_1a n dI_2

If A-B=pi//4 , then (1+t a n A)(1-t a n B) is equal to 2 b. 1 c. 0 d. 3

If I_1=int_0^pixf(sin^3x+cos^2x)dxa n d I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx , t h e n r e l a t e I_1 a n d I_2

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

The value of int_0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi

The value of int_0^pi (sin(1+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi