What is #f(x) = int 3tanx-sinx dx# if #f((7pi)/4)=12 #? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Harish Chandra Rajpoot Jul 19, 2018 #=3\ln|\sec x|+\cos x+12-3/2 \ln2-1/\sqrt2# Explanation: Given that #f(x)=\int(3\tan x-\sin x)\ dx # #f(x)=3\ln|\sec x|+\cos x+C # Given that #f({7\pi}/4)=12#, hence #12=3\ln|sec ({7\pi}/4)|+\cos({7\pi}/4)+C# #12=3\ln|\sqrt2|+1/\sqrt2+C# #C=12-3/2 \ln2-1/\sqrt2# #\therefore f(x)# #=3\ln|\sec x|+\cos x+12-3/2 \ln2-1/\sqrt2# 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 1369 views around the world You can reuse this answer Creative Commons License