What is #f(x) = int e^(2x)-2e^x+3x dx# if #f(4 ) = 2 #?

1 Answer
Steve M
Oct 18, 2016

# f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + 2e^4 - e^8/2 - 22 #

Explanation:

# f(x) = int (e^(2x) - 2e^x + 3x)dx#
# :. f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + c#

Now # f(4)=2 #
# :. e^8/2 - 2e^4 + (3(16))/2 + c = 2#
# :. e^8/2 - 2e^4 + 24 + c = 2#
# :. c = 2e^4 - e^8/2 - 22#

Hence, # f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + 2e^4 - e^8/2 - 22 #

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