Answer to Question #332677 in Calculus for Olga

Question

Integrate the following function with respect to t

 

f(t) = 0,2e^−0.2t

a.− e^−0.2t + c

b. e^−0.2t + c

c.−o.4e^−0.2t

d.−o.4e^−0.2t + c

Answer 1

$\int0.2\,e^{-0.2\,t}dt=-\int\,e^{-0.2\,t}d(-0.2t)=-e^{-0.2\,t}+C,$ $C\in{\mathbb{R}}$. We used a formula for a well-known integral $\int e^x dx$ and a substitution: $z=-0.2\,t$.

Answer: a. $-e^{-0.2\,t}+C$.