# Thread: The Fundamental Theorem of Calculus

1. ## The Fundamental Theorem of Calculus

Let g(x)= $\int_0^x f(t)dt$, where f is the function whose graph is shown.

g(0) = 0
g(3) = 4.5
g(6) =
g(9) =
g(12) =
g(15) =
g(18) =

I got the first two, but I guess I am just not getting the rest, if you could help me with how to set the up the others.

I thought g(6) you would take the 4.5 and subtract the area of the triangle that goes below the x-axis to give you -9, but the computer is telling me thats wrong. Please help!

2. Originally Posted by ryan18
Let g(x)= $\int_0^x f(t)dt$, where f is the function whose graph is shown.

g(0) = 0
g(3) = 4.5
g(6) = 0
g(9) = -4.5
g(12) = 0
g(15) = 13.5
g(18) = 36
just a process of summing signed areas between the curve and the x-axis.

integrating from left to right ... area above the x-axis is positive, area below is negative.

3. Originally Posted by ryan18
Let g(x)= $\int_0^x f(t)dt$, where f is the function whose graph is shown.

g(0) = 0
g(3) = 4.5
g(6) =
g(9) =
g(12) =
g(15) =
g(18) =

I got the first two, but I guess I am just not getting the rest, if you could help me with how to set the up the others.

I thought g(6) you would take the 4.5 and subtract the area of the triangle that goes below the x-axis to give you -9, but the computer is telling me thats wrong. Please help!
g(6) = 0 since area above y-axis = area below y-axis.

(and also, 4.5 - 9 = -4.5... hint for g(9))