Review question

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Ref: R7616

## Suggestion

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?