DaalChawal
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How Large Can This Integral Be?
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Opalg
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$|\cos(2017\theta)|\leqslant1$.
$|5-4\cos\theta|\geqslant1$.
Use those facts to estimate how large $\displaystyle\left|\int_0^\pi\frac{\cos(2017\theta)}{5-4\cos\theta}d\theta\right|$ can be. Then decide which of the four given choices seems most likely to be correct.
$|5-4\cos\theta|\geqslant1$.
Use those facts to estimate how large $\displaystyle\left|\int_0^\pi\frac{\cos(2017\theta)}{5-4\cos\theta}d\theta\right|$ can be. Then decide which of the four given choices seems most likely to be correct.