APFIVE Applying the Fundamental Theorem of Calculus
Without using a calculator, a continuous interest rate is given by $$f(t)= 0.05*t$$ (with $$t$$ in years). The additional funds gained between $$t=1$$ and $$t=4$$ can be modeled by the definite integral $$\int_{1}^{4}0.05*t\,dt$$. Which equation correctly represents this evaluation using the Fundamental Theorem of Calculus?
A
$$0.05*(4^2-1^2)$$
B
$$\frac{0.05}{2}*(4^2+1^2)$$
C
$$\frac{0.05}{2}*(4-1)$$
D
$$\frac{0.05}{2}*(4^2-1^2)$$
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