Question #99aef
2 Answers
Mar 14, 2017
Explanation:
The integrand is an odd function that is defined on
Mar 15, 2017
Recognizing the function is odd is the quickest way to do this. We could, however, integrate using integration by parts.
Explanation:
For integration by parts, let:
{(u=theta,=>,du=d theta),(dv=sec^2thetad theta,=>,v=tantheta):}
=thetatantheta+int(-sintheta)/costhetad theta
Letting
=thetatantheta+lnabscostheta+C
Then:
=pi/4tan(pi/4)+lnabscos(pi/4)-(-pi/4tan(-pi/4)+lnabscos(-pi/4))
=pi/4+ln(1/sqrt2)-pi/4-ln(1/sqrt2)
=0