I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 5.7 : Computing Definite Integrals
11. Evaluate the following integral, if possible. If it is not possible clearly explain why it is not possible to evaluate the integral.
\[\int_{0}^{\pi }{{\sec \left( z \right)\tan \left( z \right) - 1\,dz}}\] Show SolutionBe careful with this integral. Recall that,
\[\sec \left( z \right) = \frac{1}{{\cos \left( z \right)}}\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}\tan \left( z \right) = \frac{{\sin \left( z \right)}}{{\cos \left( z \right)}}\]Also recall that \(\cos \left( {\frac{\pi }{2}} \right) = 0\) and that \(x = \frac{\pi }{2}\) is in the interval we are integrating over, \(\left[ {0,\pi } \right]\) and hence is not continuous on this interval.
Therefore, this integral cannot be done.
It is often easy to overlook these kinds of division by zero problems in integrands when the integrand is not explicitly written as a rational expression. So, be careful and don’t forget that division by zero can sometimes be “hidden” in the integrand!