Calculate the investment worth in 5 years using definitive integration

Question

john whos a store manager is considering 5yr investment and estimated that t years from now it will be generating a continuous income stream of 3000 + 50t dollar per year. If the prevailing annual interest rate remains fixed at 4% compounded continuously during the entire 5 year term, what should be the investment worth in 5 years? (Future value)

where T is duration of the term, f(t) is continuous generating income per year, r is annual rate of interest.

Answer 1

FV = ∫₀^Tf(t)e^{r(T -t)}dt = ∫₀⁵(3000+ 50t)e^{0.04(5 - t)}_{dt = $17274.04.}

I use TI-84 to evaluate this integral