What is f(x) = int secx-tanx dx if f((5pi)/3) = 0 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Ratnaker Mehta Sep 22, 2016 f(x)=ln|2(2+sqrt3)(1+sinx)|. Explanation: f(x)=int(secx-tanx)dx :. f(x)=intsecxdx-inttanxdx =ln|secx+tanx|-ln|secx| =ln|(secx+tanx)/secx| =ln|secx/secx+tanx/secx| =ln|1+sinx|+c. To determine the const.c", we use the given cond. : "f(5pi/3)=0 rArr ln|1+sin(5pi/3)|+c=0 "Since, "sin(5pi/3)=sin(2pi-pi/3)=-sin(pi/3)=-sqrt3/2, so, c=-ln|1-sqrt3/2|=-ln|(2-sqrt3)/2|=ln|2/(2-sqrt3)|=ln(2(2+sqrt3)) :. f(x)=ln|1+sinx|+ln(2(2+sqrt3)), or, f(x)=ln|2(2+sqrt3)(1+sinx)|. Enjoy Maths.! 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 1352 views around the world You can reuse this answer Creative Commons License