- #1
DaalChawal
- 85
- 0
MHB How Large Can This Integral Be?
- Thread starter DaalChawal
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The integral's value is bounded by the properties of the cosine function and the denominator. Given that the absolute value of cosine is at most 1, and the denominator is always greater than or equal to 1, the integral can be estimated. The expression simplifies to analyzing the maximum possible value of the integral within the specified limits. The discussion concludes by evaluating the four provided choices to determine the most plausible estimate for the integral's size. Ultimately, the integral's maximum is constrained by the behavior of the cosine function and the properties of the denominator.
- #2
Opalg
Gold Member
MHB
- 2,778
- 13
$|\cos(2017\theta)|\leqslant1$.
$|5-4\cos\theta|\geqslant1$.
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.
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