What is f(x) = int sin^2x-cotx dx if f((5pi)/4) = 0 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Ratnaker Mehta Feb 22, 2017 f(x)=x/2-(sin2x)/4-ln|sinx|+1/4-5pi/8-1/2ln2. Explanation: f(x)=int(sin^2x-cotx)dx. :. f(x)=intsin^2xdx-intcotxdx, =int(1-cos2x)/2dx-ln|sinx|, =1/2{int1dx-intcos2xdx}-ln|sinx|, rArr f(x)=x/2-(sin2x)/4-ln|sinx|+C. "To determine "C," we use the given cond. that "f(5pi/4)=0. rArr 5pi/8-(sin(5pi/2))/4-ln|sin(5pi/4)|+C=0. rArr 5pi/8-1/4-ln|-1/sqrt2|+C=0. :. C=1/4-5pi/8-1/2ln2. Hence, f(x)=x/2-(sin2x)/4-ln|sinx|+1/4-5pi/8-1/2ln2. 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 1345 views around the world You can reuse this answer Creative Commons License