If `A= int _(0)^(1) prod_(r=1) ^(2014)(r-x) dx and B =int _(0)^(1) prod _(r =0)^(2013) (r+x) dx, ` then:

If I_(1)=int_(0)^(1)prod_(r=1)^(2016)(r-x)dx and I_(2)=int_(0)^(1)prod_(r=0)^(2015)(r+x)dx, then (I_(1))/(I_(2)) is equal to 2(b)(1)/(2)(c)-1 (d) 1

"I f"I_1=int_0^1prod_(r=1)^(2016)(r-x)dxa n dI_2=int_0^1prod_(r=0)^(2015)(r+x)dx ,t h e n(I_1)/(I_2) is equal to 2 (b) 1/2 (c) -1 (d) 1

If int _(0)^(1) (sum _(r=1) ^(2013)(x)/(x ^(2)+r ^(2)) prod_(r=1)^(2013)(x ^(2) +r ^(2) )) dx =1/2 [(prod_(r=1)^(2013)(1+r ^(2)))-k^(2)] then k=

If int _(0)^(1) (sum _(r=1) ^(2013)(x)/(x ^(2)+r ^(2)) prod_(r=1)^(2013)(x ^(2) +r ^(2) )) dx =1/2 [(prod_(r=1)^(2013)(1+r ^(2)))-k^(2)] then k=

If f(n)=prod_(r=1)^(n)cos r,n in N , then

If f(n)=prod_(r=1)^(n)cos r,n in N , then

f(x)=prod_(r=1)^(5)(x+r), then f'(-5) is

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"

If f(x) is continuous for all real values of x then sum_(r=1)^(n)int_(0)^(1)f(r-1+x)dx is equal to a) int_(0)^(n)f(x)dx b) int_(0)^(1)f(x)dx c) nint_(0)^(1)f(x)dx d) (n-1)int_(0)^(1)f(x)dx