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Category: Integration

1-sin-3xsin-x-

Question Number 17317 by palash Jana last updated on 04/Jul/17 $$\int\mathrm{1}/\sqrt{\mathrm{sin}\:\mathrm{3}{x}\mathrm{sin}\:\left({x}−\alpha\right)} \\ $$ Commented by Arnab Maiti last updated on 04/Jul/17 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{is}\int\frac{\mathrm{dx}}{\:\sqrt{\mathrm{sin}^{\mathrm{3}} \mathrm{x}\:\mathrm{sin}\left(\mathrm{x}−\alpha\right)}} \\ $$…

0-2-d-sinx-cosx-sinx-cosx-

Question Number 17255 by Arnab Maiti last updated on 02/Jul/17 $$\int_{\mathrm{0}} ^{\:\frac{\Pi}{\mathrm{2}}} \:\frac{\mathrm{d}\left(\mathrm{sinx}+\mathrm{cosx}\right)}{\mathrm{sinx}+\mathrm{cosx}} \\ $$ Answered by prakash jain last updated on 02/Jul/17 $$\mathrm{ln}\:\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)\mid_{\mathrm{0}} ^{\pi/\mathrm{2}}…

Show-that-a-b-f-kx-dx-1-k-ka-kb-f-x-dx-

Question Number 17220 by Arnab Maiti last updated on 02/Jul/17 $$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{a}} ^{\:\mathrm{b}} {f}\left(\mathrm{kx}\right)\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{k}}\int_{\mathrm{ka}} ^{\:\mathrm{kb}} {f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by ajfour last updated on 02/Jul/17 $$\mathrm{let}\:\mathrm{kx}=\mathrm{t}\:\:\:\Rightarrow\:\:\:\mathrm{dx}=\frac{\mathrm{dt}}{\mathrm{k}}…

What-will-be-the-vallu-of-a-a-x-2-y-dx-Where-x-2-y-2-a-2-and-y-0-

Question Number 17206 by Arnab Maiti last updated on 02/Jul/17 $$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{vallu}\:\mathrm{of}\:\int_{−\mathrm{a}} ^{\:\mathrm{a}} \mathrm{x}^{\mathrm{2}} \mathrm{y}\:\mathrm{dx}\:\:? \\ $$$$\mathrm{Where}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{0} \\ $$ Answered by mrW1 last…