What is f(x) = int sec^2x- cscx dx if f((5pi)/4) = 0 ?

1 Answer
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