What is #f(x) = int e^(2x)-2e^x+3x dx# if #f(4 ) = 2 #? Calculus Techniques of Integration Evaluating the Constant of Integration 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 # Answer link Related questions How do you find the constant of integration for #intf'(x)dx# if #f(2)=1#? What is a line integral? What is #f(x) = int x^3-x# if #f(2)=4 #? What is #f(x) = int x^2+x-3# if #f(2)=3 #? What is #f(x) = int xe^x# if #f(2)=3 #? What is #f(x) = int x - 3 # if #f(2)=3 #? What is #f(x) = int x^2 - 3x # if #f(2)=1 #? What is #f(x) = int 1/x # if #f(2)=1 #? What is #f(x) = int 1/(x+3) # if #f(2)=1 #? What is #f(x) = int 1/(x^2+3) # if #f(2)=1 #? See all questions in Evaluating the Constant of Integration Impact of this question 1443 views around the world You can reuse this answer Creative Commons License