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 1358 views around the world You can reuse this answer Creative Commons License