APFIVE Applying the Fundamental Theorem of Calculus
The derivative of the function $$g$$ is continuous on the closed interval $$[1,5]$$. Values of $$g$$ and $$g'$$ for selected values of $$x$$ are given in the table below:
| $$x$$ | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| $$g(x)$$ | -3 | 0 | 4 | 1 |
| $$g'(x)$$ | 2 | -1 | 3 | 5 |
If
$$\int_{1}^{5} g'(t) \,dt = 15,$$
then $$g(5) =\,$$?
A
15
B
12
C
8
D
18
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