If g is a differentiable odd function for all value of x, which one of the following statements is not NOT necessarily true?
I know that an odd function typically like an equation such as y=x³ has area under the curve of the definite integral from 0 to 2 is the same as the negative definite integral from -2 to 0. Also that odd functions whenever there is a definite integral such as -1 to 1 (or -2 to 2) is always zero. From this logic I can get rid of A) and B) as answer choices. Also I know that a constant whether inside or outside the definite integral does not change the result. When looking at answer choice C) both integrals have the schema of -4 to 4. Even if it is changed to 4 to -4 it will still result in 0. And despite being multiplied to 2 or -2 it will still be 0.
But this logic leaves d) as the only answer.
Is there any other train of thought that would allow me to directly say that D) is the answer rather than by choice elimination?
I know that an odd function typically like an equation such as y=x³ has area under the curve of the definite integral from 0 to 2 is the same as the negative definite integral from -2 to 0. Also that odd functions whenever there is a definite integral such as -1 to 1 (or -2 to 2) is always zero. From this logic I can get rid of A) and B) as answer choices. Also I know that a constant whether inside or outside the definite integral does not change the result. When looking at answer choice C) both integrals have the schema of -4 to 4. Even if it is changed to 4 to -4 it will still result in 0. And despite being multiplied to 2 or -2 it will still be 0.
But this logic leaves d) as the only answer.
Is there any other train of thought that would allow me to directly say that D) is the answer rather than by choice elimination?
