What is #f(x) = int sec^2x- cosx dx# if #f((5pi)/4) = 0 #? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer sjc Dec 11, 2016 #f(x)=tanx-sinx-(1+sqrt2/2)# Explanation: #int(sec^2x-cosx)dx# #f(x)=tanx-sinx+c# #f((5pi)/4)=tan((5pi)/4)-sin((5pi)/4)+c=0# #1-(-sqrt2/2)+c=0# #c=-(1+sqrt2/2)# #f(x)=tanx-sinx-(1+sqrt2/2)# 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 1231 views around the world You can reuse this answer Creative Commons License