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IntegrationQuestion and Answers: Page 19
Question Number 200257 Answers: 1 Comments: 0
Question Number 200256 Answers: 0 Comments: 0
Question Number 200254 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:{calculate}\:... \\ $$$$\:\:\Omega\:=\:\int_{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{tan}\left({x}\right)\right){dx}} ^{\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx}} \mathrm{ln}\left(\mathrm{sin}\left({x}\right)\right){dx}=? \\ $$
Question Number 200253 Answers: 2 Comments: 0
Question Number 200250 Answers: 2 Comments: 0
Question Number 200159 Answers: 1 Comments: 2
Question Number 200155 Answers: 2 Comments: 0
Question Number 200130 Answers: 2 Comments: 0
$$\:\:{solve}\:{by}\:{contour}\:{integrstion} \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{\mathrm{1}+{a}\mathrm{cos}{x}}\: \\ $$
Question Number 200048 Answers: 0 Comments: 2
Question Number 200061 Answers: 1 Comments: 0
$$\:\:\:\:\int_{−\infty} ^{+\infty} \frac{{x}\mathrm{sin}{x}\:}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}\:\:=\:\:\:?? \\ $$
Question Number 199942 Answers: 1 Comments: 0
Question Number 199934 Answers: 2 Comments: 0
$$\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$$$ \\ $$
Question Number 199921 Answers: 1 Comments: 0
Question Number 199907 Answers: 1 Comments: 0
$$\:\:\:\:\:\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:=?\: \\ $$
Question Number 199903 Answers: 2 Comments: 1
$$\int\frac{{x}^{\mathrm{2}} {dx}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{16}}}\:=\:? \\ $$
Question Number 199598 Answers: 0 Comments: 0
Question Number 199570 Answers: 1 Comments: 0
$$\:\:\:\:\:\:\:\:\mathrm{I}\:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}{x}\:}{\mathrm{2}}\right){dx} \\ $$
Question Number 199471 Answers: 1 Comments: 0
$${Find}\:{the}\:{integral} \\ $$$$\int_{−\mathrm{3}} ^{\mathrm{3}} \begin{cases}{{x}^{\mathrm{3}} −{x}}&{\left({x}\leq\mathrm{0}\right)}\\{{x}^{\mathrm{2}} }&{\left({x}\geq\mathrm{0}\right)}\end{cases}{dx} \\ $$
Question Number 199468 Answers: 1 Comments: 0
Question Number 199377 Answers: 1 Comments: 0
$$\:\:\int\underset{\mathrm{R}} {\int}\mathrm{cos}\:\left(\mathrm{max}\left\{\mathrm{x}^{\mathrm{3}} ,\:\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right\}\right)\mathrm{dx}\:\mathrm{dy}\:,\:\mathrm{where}\:\mathrm{R}\:=\:\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$
Question Number 199369 Answers: 0 Comments: 0
$$\int_{−\mathrm{1}} ^{\mathrm{1}} \:\int_{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} ^{\mathrm{1}+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} {dx}\:{dy}\:{dz}\:\:{is} \\ $$
Question Number 199213 Answers: 1 Comments: 0
Question Number 199162 Answers: 0 Comments: 0
$${x}=−\mathrm{2}\sqrt{\mathrm{3}}\int{y}^{\mathrm{3}} \sqrt{\mathrm{1}+\frac{\mathrm{1}}{{y}}}\:{dy} \\ $$$${Find}\:\:\int{x}\left({y}\right){dy}\:\:\:. \\ $$
Question Number 198948 Answers: 2 Comments: 0
$$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −\mathrm{4x}}\:\mathrm{dx}=\:.... \\ $$
Question Number 198929 Answers: 0 Comments: 0
Question Number 198802 Answers: 1 Comments: 0
$$\mathrm{radius}\:{r}\:\mathrm{circle}\:;\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\hat {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)={yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{x}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xy}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\mathrm{Find}\:\mathrm{flux}\:\boldsymbol{\rho}=\int\int_{\:\boldsymbol{\Sigma}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\hat {\boldsymbol{\mathrm{n}}}\:\mathrm{d}{S} \\ $$
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