If f and g are continuousfunctions and g'(x)=f(x) for all x,then the integral from interval 2 to 3 of f(x)dx=?

Answer 1

g(3) - g(2).

This is the Fundamental Theorem of Calculus.

Answer 2

-you'd have to set up an integral with upper bound 3 and lower bound 2.
-and you know that if g'(x)=f(x), then g(x)= integral of f(x)
-then using the Fundamental Theorem of Calculus, you'd first have to plug in 3 into the integral of the f(x) equation (aka g(3)) and subtract from that the same equation except with 2 plugged in. it would look like this:
1) set the equation:
3
∫ f(x) dx
2
2) [g(x)] upper:3, lower: 2
3) g(3)-g(2)

hope this helps
I'm in calculus too :)

Answer 3

g(3) - g(2)

Answer 4

g(3) - g(2). sice f is the derivative of g, g is the integral of f.