F is a differentiable function for all x. Which of the following statements must be true? a. d/dx ∫ f(x)dx=f(x)
b. d/dx ∫ f(t)dt= - f(x)
c. ∫ f′(x)dx=−f(x)

The limits in the integral of the options are missing. They are :

a).

b).

c).

Solution:

We known that

a).  

     = 0 - 0

     = 0

Hence it is true.

b).  

      = f(x)

Hence it is true.

c).

Hence it is false.

Therefore option a) and b). are true.

do you have the measurements?