Let \[T=\left( \int _{-\pi/2}^{\pi/2}\cos x\,dx\right)\times \left(\int_\pi ^{2\pi} \sin x\,dx\right) \times \left(\int_0^{\pi/8}\frac{dx}{\cos 3x}\right).\] Which of the following is true?

  1. \(T=0\);

  2. \(T<0\);

  3. \(T>0\);

  4. \(T\) is not defined.

Note that the third integral, \(\displaystyle \int_0^{\pi/8}\frac{dx}{\cos 3x}\), means the same as \[\int_0^{\pi/8}\frac{1}{\cos 3x}\,dx.\]

Do we need to work out the exact values of each of the integrals? What is the important thing to know?