Question

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

Answer 1

`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`