int_(-51)^(51)(dx)/(3+f(x))

Let f be a function such that f(x).f\'(-x)=f(-x).f\'(x) for all x and f(0)=3 . Now answer the question: int_-51^51dx/(3+f(x))= (A) 34 (B) 102 (C) 0 (D) 17

If f(2-x)=f(2+x) and f(4-x)=f(4+x) for all x and f(x) is a function for which int_(0)^(2)f(x)dx=5, then int_(0)^(50)f(x)dx is equal to 125 (b) int_(-4)^(46)f(x)dx int_(1)^(51)f(x)dx(d)int_(2)^(52)f(x)dx

Match the following {:("List - 1","List - II"),("I) "int_(-1)^(1)x|x|dx,"a) "(pi)/(2)),("II) "int_(0)^((pi)/(2))(1+log((4+3sinx)/(4+3cosx)))dx,"b) "int_(0)^((pi)/(2))f(x)dx),("III) "int_(0)^(a)f(x)dx,"c) "int_(0)^(a)[f(x)+f(-x)]dx),("IV) "int_(-a)^(a)f(x)dx,"d) "0),(,"e) "int_(0)^(a)f(a-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

int_(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-3x)/3))dx=

int_(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-3x)/3))dx=

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 125 (b) int_(-4)^(46)f(x)dx int_1^(51)f(x)dx (d) int_2^(52)f(x)dx

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 int_(-3)^(2)f(x) dx= 7/3 and int_(-3)^(9) f(x) dx = -5/6 , then what is the value of int_(2)^(9)f(x) dx ?

If int_(-3)^(2) f(x)dx= 7/3 and int_(-3)^(9) f(x)dx= - 5/6 then int_(2)^(9) f(x)dx=