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IntegrationQuestion and Answers: Page 147
Question Number 110551 Answers: 2 Comments: 0
Question Number 110549 Answers: 2 Comments: 1
Question Number 110543 Answers: 1 Comments: 0
Question Number 110888 Answers: 3 Comments: 0
$$\:\:\:\:\:\:\:\:\:\:....{calculus}.... \\ $$$${please}\:{solve}\:: \\ $$$$ \\ $$$$\Omega_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \left(\sqrt{{tan}\left({x}\right)}\:+\sqrt{{cot}\left({x}\right)}\:\right){dx}=?? \\ $$$$\:\Omega_{\mathrm{2}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {tan}\left({x}\right){ln}\left(\left(\mathrm{1}+{tan}^{\mathrm{2}} \left({x}\right)\right)\right){dx}\:=?? \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:...\mathscr{M}.\mathscr{N}.{july}\:\mathrm{1970}#... \\ $$$$\:\mathscr{G}{ood}\:{luck} \\ $$$$ \\ $$$$ \\ $$
Question Number 110451 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\mathrm{U}_{\mathrm{n}} =\int_{\left[\frac{\mathrm{1}}{\mathrm{n}},\mathrm{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} } \mathrm{dxdy} \\ $$$$\mathrm{and}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$
Question Number 110450 Answers: 1 Comments: 0
$$\mathrm{find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3y}^{\mathrm{2}} \right)\:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{3y}^{\mathrm{2}} } \:\mathrm{dxdy} \\ $$
Question Number 110448 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4i}\right)^{\mathrm{3}} }\mathrm{dx}\:\:\:\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$
Question Number 110447 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{ix}\:+\mathrm{1}\right)^{\mathrm{2}} }\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$
Question Number 110301 Answers: 0 Comments: 1
Question Number 110262 Answers: 0 Comments: 0
$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right) \\ $$$$\begin{cases}{\frac{\partial\mathrm{Z}}{\partial\mathrm{y}}−\frac{\partial\mathrm{Y}}{\partial\mathrm{z}}=\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\\{\frac{\partial\mathrm{Z}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{z}}=−\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\\{\frac{\partial\mathrm{Y}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{y}}=\mathrm{z}\left(\mathrm{2x}−\mathrm{y}\right)}\end{cases}\:\mathrm{where}\:\begin{cases}{\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\end{cases} \\ $$
Question Number 110247 Answers: 1 Comments: 0
$$\mathrm{Let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\:{x}} {e}^{−{t}} {dt}\: \\ $$$$\mathrm{then}\:{f}\:''\left({x}\right)\:=\:?? \\ $$
Question Number 110245 Answers: 1 Comments: 2
$${solve}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{c}−\sqrt{{b}−{ax}}}} \\ $$
Question Number 110233 Answers: 0 Comments: 0
Question Number 110218 Answers: 1 Comments: 0
Question Number 110215 Answers: 1 Comments: 1
Question Number 110203 Answers: 1 Comments: 0
Question Number 110143 Answers: 2 Comments: 0
Question Number 110027 Answers: 2 Comments: 0
Question Number 109989 Answers: 1 Comments: 1
Question Number 109988 Answers: 0 Comments: 0
Question Number 109949 Answers: 1 Comments: 0
Question Number 109891 Answers: 1 Comments: 0
$$\:\:\frac{\Delta{be}\bigtriangledown}{{math}} \\ $$$$\int\:\frac{\mathrm{arc}\:\mathrm{tan}\:{x}}{\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)}\:{dx}\:? \\ $$
Question Number 109884 Answers: 1 Comments: 1
Question Number 109872 Answers: 2 Comments: 1
$$\:\:\frac{\bigstar{be}\bigstar}{\mathcal{M}{ath}} \\ $$$$\int\:\frac{\mathrm{cos}\:{x}\:{dx}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{4sin}\:{x}−\mathrm{5}}\:? \\ $$
Question Number 109849 Answers: 0 Comments: 0
Question Number 109839 Answers: 4 Comments: 1
$$\:\frac{{JS}}{\approx\heartsuit\approx} \\ $$$$\left(\mathrm{1}\right)\:\int\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}\:{dx} \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\sqrt{\mathrm{tan}\:{x}}\:}\:{dx}\: \\ $$
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