Question #332677

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



1
Expert's answer
2022-05-03T09:18:47-0400

0.2e0.2tdt=e0.2td(0.2t)=e0.2t+C,\int0.2\,e^{-0.2\,t}dt=-\int\,e^{-0.2\,t}d(-0.2t)=-e^{-0.2\,t}+C, CRC\in{\mathbb{R}}. We used a formula for a well-known integral exdx\int e^x dx and a substitution: z=0.2tz=-0.2\,t.

Answer: a. e0.2t+C-e^{-0.2\,t}+C.


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