If `f(x)=x if x<1 and f(x)=x-1 if x>=1`,then `int_0^2 x^2 f(x) dx` is (a)1 (b)`4/3 (c)5/3 (d)5/2`

If f(x)+f(3-x)=0 ,then int_(0)^(3)1/(1+2^(f(x)))dx=

If f(x)+f(3-x)=0 , then int_(0)^(3)1/(1+2^(f(x)))dx=

If int_(-1)^(4) f(x) dx=4 and int_(2)^(4) (3-f(x))dx=7 , then int_(-1)^(2) f(x)dx is a)1 b)2 c)3 d)5

[ If f(x)=|x|+|x-1|, then int_(0)^(2)f(x)dx equals- [ (A) 3, (B) 2, (C) 0, (D) -1]]

Let f : R->R be given by f(x) = {|x-[x]| , when [x] is odd and |x-[x]-1| , when [x] is even ,where [.] denotes the greatest integer function , then int_-2^4 f(x) dx is equal to (a) (5)/(2) (b) (3)/(2) (c) 5 (d) 3

If f(6-x)=f(x), for all x, then 1/5 int_2^3 x[f(x)+f(x+1)]dx is equal to :

If int f(x)dx=psi(x), then int x^(5)f(x^(3))dxint x^(5)f(x^(3))dx(1)/(3)x^(3)psi(x^(3))-3int x^(3)psi(x^(3))dx+C(2)(1)/(3)x^(3)psi(x^(3))-int x^(3)psi(x^(3))dx+C(3)(1)/(3)x^(3)psi(x^(3))-int x^(3)psi(x^(3))dx+C(4)(1)/(3)[x^(3)psi(x^(3))-int x^(2)psi(x^(3))dx]+C

Iff(2-x)=f(2+x)a n df(4-x)=f(4+x) for all xa n df(x) is a function for which int_0^2f(x)dx=5,t h e nint_0^(50)f(x)dx is equal to (a)125 (b) int_(-4)^(46)f(x)dx (c) int_1^(51)f(x)dx (d) int_2^(52)f(x)dx

If f(x) is differentiable and int_0^(t^2) x f(x) dx=2/5t^5, then f(4/(25)) equals (a) 2/5 (b) -5/2 (c) 1 (d) 5/2

If f(x) is differentiable and int_0^(t^2) x f(x) dx=2/5t^5, then f(4/(25)) equals (a) 2/5 (b) -5/2 (c) 1 (d) 5/2