If `f(x) = pe^(2x) + qe^x + rx` satisfies the condition `f(0)=-1, f' (In 2)=31 and int_0^(In4) (f(x)-rx)dx=39/2`, then the value of `(p+q+ r)` is equal to

If f(x) =ae^(2x)+be^(x)+cx , satisfies the conditions f(0)=-1, f'(log 2)=31, int_(0)^(log4) (f(x)-cx)dx=(39)/(2) , then

If f(x)=Ax^(2) +Bx satisfies the conditions f^(1)(1)=8 and int_(0)^(1) f(x)dx=8/3 , then

If f(x)=ae^(2x)+be^(x)+cx satisfies the condition f(0)=ae^(2x)+be^(x)+cx satisfies the condition f(0)=-1, f'(log2)=31,int_(0)^(log4)(f(x)-cx)dx=(39)/(2) , then

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) satisfies the conditions of Rolle's Theorem on [1,2] , then int_1^2 f'(x) dx equals:

If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3