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Question Number 207723 by SANOGO last updated on 24/May/24

$$\mathrm{li}m{\int }_0^{\mathrm{\infty }}(1-e^{-ncos\left(x\right)})dx$$

Commented by Frix last updated on 24/May/24

$$f\left(x\right)=1-{\mathrm{e}}^{-n\cos x}$$$$n\to \mathrm{\infty }\Rightarrow f\left(x\right)=\{\begin{array}{l}1;-\frac{\pi }{2}+k\pi ⩽x⩽\frac{\pi }{2}+k\pi \\ -\mathrm{\infty };\frac{\pi }{2}+k\pi <x<\frac{3\pi }{2}+k\pi \end{array}\mathrm{\forall }k\in \mathbb{Z}$$$$\mathrm{This}\mathrm{integral}\mathrm{cannot}\mathrm{converge}.$$

Commented by SANOGO last updated on 25/May/24

$$thankyou$$

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