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Applying the Fundamental Theorem of Calculus

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The accumulation of interest on an investment from year t=1t=1 to year t=4t=4 is modeled by the definite integral ∫140.05∗t dt\int_{1}^{4} 0.05*t\,dt. According to the Fundamental Theorem of Calculus, which of the following expressions represents the value of this integral?

A

0.052∗(4−1)\frac{0.05}{2}*(4-1)

B

0.05∗(42−12)0.05*(4^2-1^2)

C

0.052∗(42+12)\frac{0.05}{2}*(4^2+1^2)

D

0.052∗(42−12)\frac{0.05}{2}*(4^2-1^2)

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