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

1 Answer
Feb 26, 2017

f(x)=1/8(2sin2x-4+5pi-10)+tanx

Explanation:

f(x)=intsec^2x-cos^2x dx, f(5/4pi)=0

f(x)=intsec^2x-cos^2x dx=intsec^2x dx-intcos^2x dx=
tanx+1/4(sin2x-2x)+"C"

f(5/4pi)=0=tan(5/4pi)+1/4(sin(5/2pi)-5/2pi)+"C"=
1+1/4-5/8pi+"C"=0

"C"=(5pi-10)/8

f(x)=tanx+1/4(sin2x-2x)+(5pi-10)/8=
1/8(2sin2x-4+5pi-10)+tanx