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proof-that-0-pi-4-sin-2-xcos-2-x-sin-3-x-cos-3-x-2-dx-1-6-




Question Number 108306 by Sayantan chakraborty last updated on 16/Aug/20
proof that ∫_(0) ^(π/4) ((sin^2 xcos^2 x)/((sin^3 x+cos^3 x)^2 )) dx =(1/6)
$$\mathrm{proof}\:\mathrm{that}\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{{sin}^{\mathrm{2}} {xcos}^{\mathrm{2}} {x}}{\left({sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}\right)^{\mathrm{2}} }\:{dx}\:=\frac{\mathrm{1}}{\mathrm{6}} \\ $$

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