The function `f` is continuous and has the property `f(f(x))=1-x " for all" x in [0,1] and f=int _(0)^(1)f(x) dx `, then

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) f(1/3).f(2/3)=1 (C) the value of J equals to 1/2 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

The function of f is continuous and has the property f(f(x))=1-xdot Then the value of f(1/4)+f(3/4) is

The function of f is continuous and has the property f(f(x))=1-xdot Then the value of f(1/4)+f(3/4) is

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

If f(x) is a continuous function such that f(x) gt 0 for all x gt 0 and (f(x))^(2020)=1+int_(0)^(x) f(t) dt , then the value of {f(2020)}^(2019) is equal to

Let f:[1,2] to [0,oo) be a continuous function such that f(x)=f(1-x) for all x in [-1,2]. Let R_(1)=int_(-1)^(2) xf(x) dx, and R_(2) be the area of the region bounded by y=f(x),x=-1,x=2 and the x-axis . Then,

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. The length of the subtangent of the curve y= f (x ) at x=1//2 is:

Let f(x) be a continuous function and I = int_(1)^(9) sqrt(x)f(x) dx , then

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. b=