Question

solve problem using the fundamental theorem of calculus:
f'(x)=e^(-x) and f(5)=1. Find f(2).
Please and thank you :)

Answer 1

\[f(x)=\int\limits_{}^{}e^{-x} dx+C=-e^{-x}+C\]

Answer 2

\[f(5)=-e^{-(5)}+C=1\]

Answer 3

so we have enough info to solve for C

Answer 4

\[-e^{-5}+C=1 => C=1+e^{-5} => f(x)=-e^{-x}+(1+e^{-5})\]

Answer 5

See this is a cal 1 problem not the type of question you posted earlier

Answer 6

\[f(2)=-e^{-(2)}+(1+e^{-5})=e^{-5}-e^{-2}+1\]

Answer 7

oh.....I get it now... It makes complete sense. thank you :)