[" If "x=f''(t)cos t+f'(t)sin t" and "y=-f''(t)sin t+f'(t)cos t],[" then "int[((dx)/(dt))^(2)+((dy)/(dt))^(2)]^(1/2)dt" equals "]

If =f''(t)cos t+f'(t)sin t,y=-f''(t)sin t+f'(t)cos t, then int[((dx)/(dt))^(2)+((dy)/(dt))^(2)]^((1)/(2))dt is equal to

If x=f(t )cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2

If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ((dx)/(dt))^2+((dy)/(dt))^2= f(t)-f"(t) (b) {f(t)-f"(t)}^2 (c) {f(t)+f"(t)}^2 (d) none of these

If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ((dx)/(dt))^2+((dy)/(dt))^2= f(t)-f"(t) (b) {f(t)-f"(t)}^2 (c) {f(t)+f"(t)}^2 (d) none of these

If x= f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2 (a) f(t)-f^(primeprime)(t) (b) {f(t)-f^(primeprime)(t)}^2 (c) {f(t)+f^(primeprime)(t)}^2 (d) none of these

cos t dx/dt + sin t = 1

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -

Let f(t)=sqrt(1-sin t), then int_(0)^(2 pi)f(t)*dt-int_(0)^( pi)f(t).dt, is equal to