Applications of the Definite Integral
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Future Value of a continuous income stream Formula :

 ∫^{N}_{0} Kdt
 K = dollars per year
 N = years at interest rate r
 r = interest rate
Example 1 :
 At an annual rate of $1000, money is being deposited into a savings account everyday. The savings account pays 6% interest that is compounded continuously. What is approximately the amount of money in the account after 5 years?
 Solution :
 ∫^{5}_{0}dt
 = ^{5}_{0}
 =
 = approximately = 5831
 ∫^{5}_{0}dt
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