i don't understand this, Show that if G(x) is an antiderivitive for f(X) and G(2)=-2 then G(4)=-7+((integral))top number 4 lower number 2 f(X)dx

its so confusing.? HELP. Thanks!!

There is a fundamental theorem oc calculaus that states that the integral of f(x)dx from a to b is

G(b) - G(a). This assumes than f is the derivative of G (or G is the integral of f).
Therefore
G(4) = G(2) + integral(2 to 4)of f(x)dx

What you wrote is not correct. The -7 should be -2.

so does this mean that the equation is incorrect, or it is like undefined. That is exactly how it is in the paper, and it says to explain why it is right? So do i write it is incorrect.

To solve this problem, we need to use the Fundamental Theorem of Calculus, which states that if F(x) is an antiderivative of f(x) on an interval [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a).

In this problem, we are given that G(x) is an antiderivative of f(x), and we are also given the value of G(2) as -2. Let's start by writing down the equation using the Fundamental Theorem of Calculus:

∫[2 to 4] f(x) dx = G(4) - G(2)

We want to find G(4), and we are given G(2) as -2. To solve for G(4), we can rearrange the equation:

G(4) = ∫[2 to 4] f(x) dx + G(2)

Now, let's look at the second part of the equation: ∫[2 to 4] f(x) dx. This represents the definite integral of f(x) from x = 2 to x = 4. It calculates the area under the curve of f(x) between x = 2 and x = 4.

To evaluate this integral, we need to know the function f(x). Once we have the function, we can integrate it with respect to x from 2 to 4. The result will be a number, which we will add to G(2) to find G(4).

Unfortunately, the problem statement does not provide the function f(x), so we can't continue any further without that information. If you have the function f(x), please provide it so we can proceed with the solution.