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Category: Integration

let-f-a-0-cos-x-2-sin-x-2-x-2-a-2-2-dx-with-a-gt-0-1-calculate-f-a-2-find-the-values-of-0-cos-x-2-sin-x-2-x-2-1-2-and-0-cos-x-2-sin-x-2-

Question Number 64993 by mathmax by abdo last updated on 23/Jul/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)−{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({x}^{\mathrm{2}}…

xe-1-2x-dx-

Question Number 130512 by MJS_new last updated on 26/Jan/21 $$\int{x}\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}{x}}} {dx}=? \\ $$ Commented by Dwaipayan Shikari last updated on 26/Jan/21 $$\frac{\mathrm{1}}{\mathrm{2}{x}}=−{t}\Rightarrow\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }=\frac{{dt}}{{dx}} \\ $$$$=−\mathrm{2}\int{x}^{\mathrm{3}}…

Question-64975

Question Number 64975 by Tawa1 last updated on 23/Jul/19 Commented by Prithwish sen last updated on 23/Jul/19 $$\int\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}+….} \mathrm{dx}\:=\int\mathrm{x}^{\sqrt{\mathrm{e}}−\mathrm{1}} \mathrm{dx}\:\mathrm{and}\:\mathrm{proceed} \\ $$ Terms…

let-f-a-0-cos-x-2-sin-x-2-x-2-a-2-2-dx-with-a-gt-0-1-calculate-f-a-2-find-the-values-of-0-cos-x-2-sin-x-2-x-2-1-2-dx-and-0-cos-x-2-sin-x-2-

Question Number 64970 by mathmax by abdo last updated on 23/Jul/19 $${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)\:+{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}}…

0-x-cos-t-sin-3-t-1-4-sin-x-sin-t-3-4-dt-

Question Number 130486 by benjo_mathlover last updated on 26/Jan/21 $$\:\int_{\mathrm{0}} ^{\:{x}} \:\frac{\mathrm{cos}\:{t}\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{3}} \:{t}}}{\left(\mathrm{sin}\:{x}−\mathrm{sin}\:{t}\right)^{\mathrm{3}/\mathrm{4}} }\:{dt}\:? \\ $$ Answered by MJS_new last updated on 26/Jan/21 $$\int\mathrm{cos}\:{t}\:\left(\frac{\mathrm{sin}\:{t}}{\mathrm{sin}\:{x}\:−\mathrm{sin}\:{t}}\right)^{\mathrm{3}/\mathrm{4}} {dt}=…

Integrate-the-function-f-x-y-xy-x-2-y-2-over-the-domain-R-3-x-2-y-2-3-1-y-4-

Question Number 130478 by liberty last updated on 26/Jan/21 $$\:{Integrate}\:{the}\:{function}\:{f}\left({x},{y}\right)={xy}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right) \\ $$$${over}\:{the}\:{domain}\:{R}=\left\{−\mathrm{3}\leqslant{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \leqslant\mathrm{3},\:\mathrm{1}\leqslant{y}\leqslant\mathrm{4}\:\right\} \\ $$ Answered by EDWIN88 last updated on 26/Jan/21…