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 int_(0)^(x)f(t)dt=x^2+int_(x)^(1)\ t^2\ f(t)dt , then f((1)/(2)) is equal to (a) (24)/(25) (b) (4)/(25) (c) (4)/(5) (d) (2)/(5)

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+x y)dx""=x""dy , then f(-1/2) is equal to: (1) -2/5 (2) -4/5 (3) 2/5 (4) 4/5

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 an invertible function and g(x)=2f(x)+5, then the value of g^(-1)(x)i s (a) 2f^(-1)(x)-5 (b) 1/(2f^(-1)(x)+5) 1/2f^(-1)(x)+5 (d) f^(-1)((x-5)/2)

If f(x) is an invertible function and g(x)=2f(x)+5, then the value of g^(-1)(x)i s (a) 2f^(-1)(x)-5 (b) 1/(2f^(-1)(x)+5) 1/2f^(-1)(x)+5 (d) f^(-1)((x-5)/2)

Let f(x) be a differentiable function such that int_(t)^(t^(2))xf(x)dx=(4)/(3)t^(3)-(4t)/(3)AA t ge0 , then f(1) is equal to

If 2f(x)-3f(1/x)=x^2(x!=0), then f(2) is equal to (a) -7/4("b")""5/2 (c) -1 (d) none of these

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to : (a) 0 (b) 2e (c) 2e^2 -2 (d) e^2-e

If f is continuous function and F(x)=int_0^x((2t+3)*int_t^2f(u)d u)dt , then |(F''(2))/(f(2))| is equal to_____

Differentiate the following w.r.t x x^(5//2)