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Category: Integration

calculate-in-terms-of-x-f-x-0-pi-2-dt-1-xsint-

Question Number 27184 by abdo imad last updated on 02/Jan/18 $${calculate}\:{in}\:{terms}\:{of}\:{x}\:\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}\:}} \frac{{dt}}{\mathrm{1}+{xsint}}\:. \\ $$ Commented by abdo imad last updated on 05/Jan/18 $${let}\:{do}\:{the}\:{changement}\:\:{tan}\left(\frac{{t}}{\mathrm{2}}\right)=\:\alpha\Leftrightarrow{t}=\mathrm{2}{arctan}\alpha \\…

find-the-value-of-I-a-D-a-e-x-2-y-2-2-dxdy-with-D-a-x-y-R-2-x-2-y-2-a-2-

Question Number 27182 by abdo imad last updated on 02/Jan/18 $$\:{find}\:{the}\:{value}\:{of}\:{I}_{{a}} =\:\int\int_{{D}_{{a}} } {e}^{−\frac{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{\mathrm{2}}} {dxdy}\:\:{with} \\ $$$${D}_{{a}} \:=\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} \:/\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\:{a}^{\mathrm{2}} \:\:\right\} \\…

find-the-value-of-D-x-2-y-2-dxdy-with-D-x-y-R-2-1-x-2-and-1-x-y-x-

Question Number 27180 by abdo imad last updated on 02/Jan/18 $${find}\:{the}\:{value}\:{of}\:\:\int\int_{{D}} \:\:\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:{dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x}\:,{y}\right)\in\mathbb{R}^{\mathrm{2}} \:/\:\:\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:\:{and}\:\:\frac{\mathrm{1}}{{x}}\leqslant{y}\leqslant\:{x}\:\:\right\}. \\ $$ Commented by abdo imad last updated…

Question-158207

Question Number 158207 by tounghoungko last updated on 01/Nov/21 Answered by qaz last updated on 01/Nov/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{x}^{\mathrm{5}} \left(\mathrm{e}^{\mathrm{3x}} −\mathrm{e}^{\mathrm{x}} \right)}{\left(\mathrm{e}^{\mathrm{x}} −\mathrm{1}\right)^{\mathrm{4}} }\mathrm{dx} \\…

0-p-x-c-x-dx-

Question Number 92668 by john santu last updated on 08/May/20 $$\underset{\mathrm{0}} {\overset{\mathrm{p}} {\int}}\:\sqrt{\frac{\mathrm{x}}{\mathrm{c}−\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$ Commented by john santu last updated on 08/May/20 $$\mathrm{set}\:\mathrm{t}\:=\:\sqrt{\frac{{x}}{{c}−{x}}}\:,\:{x}\:=\:\frac{{ct}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}}…