If `f(x)=(sin([x]pi))/(x^2+x+1)` , where `[dot]` denotes the greatest integer function, then `fi son eon e` `fi snoton e-on ea n dnon-con s t a n t` `fi sacon s t a n tfu n c t ion` `non eoft h e s e`

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

int_0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer function and x in R^+ , is equal to

f(x)=sin^(-1)[e^(x)]+sin^(-1)[e^(-x)] where [.] greatest integer function then

If p=(8+3sqrt(7))^n a n df=p-[p],w h e r e[dot] denotes the greatest integer function, then the value of p(1-f) is equal to 1 b. 2 c. 2^n d. 2^(2n)

Find the value of : int_0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denotes the greatest integer function).

Let f(x)=[n+p sin x], x in (0, pi) n in Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f(x) is not differentiable.

Consider two curves C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y , where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is (a) 8/3s qdotu n i t s (b) (10)/3s qdotu n i t s (c) (11)/3s qdotu n i t s (d) (11)/4s qdotu n i t s

The range of f(x)=[1+sinx]+[2+sin(x/2)]+[3+sin (x/3)]+....+[n+sin (x/n)]AAx in [0,pi] , where [.] denotes the greatest integer function, is,

Evaluate: int_0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[dot] denotes the greatest integer function.

int_0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,a n d[dot] denotes the greatest integer function . then the value of f(1/pi) is