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Question-206639




Question Number 206639 by mathlove last updated on 21/Apr/24
Commented by Frix last updated on 21/Apr/24
=∫_(π/(12)) ^(π/(11)) (((√s)/(2((√c)+(√s))))−((√(cs))/(c+(√s)((√c)+1)))+((((√c)−1)s+(√(cs)))/(2(((√s)+1)c+((√c)+1)s))))dx  With c=cos x ∧s=sin x  I doubt we can solve this.
$$=\underset{\frac{\pi}{\mathrm{12}}} {\overset{\frac{\pi}{\mathrm{11}}} {\int}}\left(\frac{\sqrt{{s}}}{\mathrm{2}\left(\sqrt{{c}}+\sqrt{{s}}\right)}−\frac{\sqrt{{cs}}}{{c}+\sqrt{{s}}\left(\sqrt{{c}}+\mathrm{1}\right)}+\frac{\left(\sqrt{{c}}−\mathrm{1}\right){s}+\sqrt{{cs}}}{\mathrm{2}\left(\left(\sqrt{{s}}+\mathrm{1}\right){c}+\left(\sqrt{{c}}+\mathrm{1}\right){s}\right)}\right){dx} \\ $$$$\mathrm{With}\:{c}=\mathrm{cos}\:{x}\:\wedge{s}=\mathrm{sin}\:{x} \\ $$$$\mathrm{I}\:\mathrm{doubt}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}. \\ $$

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