What is #f(x) = int sec^2x- cscx dx# if #f((5pi)/4) = 0 #? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Nam D. Apr 8, 2018 #f(x)=tan(x)-ln|tan(x/2)|+ln|-sqrt2-1|-1# Explanation: We got: #f(x)=intsec^2x-cscx \ dx# #=intsec^2x \ dx-intcscx \ dx# #=tan(x)-ln|tan(x/2)|+C# Also, we know that #f((5pi)/4)=0#, and we have to find #C#. #f((5pi)/4)=0# #=>tan((5pi)/4)-ln|tan(((5pi)/4)/2)|+C=0# #=>tan((5pi)/4)-ln|tan((5pi)/8)|+C=0# #=>1-ln|-sqrt2-1|+C=0# #:.C=ln|-sqrt2-1|-1# #:.f(x)=tan(x)-ln|tan(x/2)|+ln|-sqrt2-1|-1# 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 1275 views around the world You can reuse this answer Creative Commons License