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Results tagged with integration
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user 385646
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
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How to find the exact value of $\int_{0}^{\pi} \ln (b \cos x+c)$ without Feynman’s Technique... [closed]
I shall find the integral by Feynman’s Technique Integration on a particular integral
$\displaystyle I(a)=\int_{0}^{\pi} \ln (a \cos x+1) d x,\tag*{} $
where $-1\leq a \leq 1.$
$\displaystyle \begin{aligned … $
\int_{0}^{\pi} \ln (\cos x+1)=2 \pi \ln \left(\frac{1}{\sqrt{2}}\right)=-\pi \ln 2;
$$
$$
\int_{0}^{\pi} \ln (\sqrt{3} \cos x+2) d x=\pi\ln \frac{3}{2}
$$
Is there any method other than Feynman’s integration …
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