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?
\(T=0\);
\(T<0\);
\(T>0\);
\(T\) 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?
