Let `f(x)` be a function defined on R such that `f^(prime)(x)=f^(prime)(3-x)AA x in [0, 3] with f(0)=-32 and f(3)-46.` Then find the value of `int_0^3f(x)dx.`

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

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

Let f be a derivable function on [0,3] such that f'(x)<=1AA x in[0,3] where f(0)=0&f(3)=3 then f(1)=

Let f be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,and f(0)=3, and if f(3)=3, then the value of f(-3) is ______________

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,and f(0)=3, and if f(3)=3, then the value of f(-3) is ______________

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x)for a l lx ,a n df(0)=3,a n dif f(3)=3, then the value of f(-3) is ______________

If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime)(x)fora l lx ,a n df(0)=3,a n diff(3)=3, then the value of f(-3) is ______________

If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime)(x)fora l lx ,a n df(0)=3,a n diff(3)=3, then the value of f(-3) is ______________

Let f(x) be a function such that f'((1)/(x))+x^(3)f'(x)=0. What is int_(-1)^(1)f(x)dx