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Question Number 220790 Answers: 1 Comments: 0

Complex integral ∮_( C) (dz/(z^3 +1))=?? , C;x^2 +y^2 =4 ∮_( C) (1/z)e^z dz, C; { ((y=1 , −1≤x≤1)),((y=−1 , −1≤x≤1)),((x=1 , −1≤y≤1)),((x=−1 , −1≤y≤1)) :}

$$\mathrm{Complex}\:\mathrm{integral} \\ $$$$\oint_{\:\mathrm{C}} \:\frac{\mathrm{d}{z}}{{z}^{\mathrm{3}} +\mathrm{1}}=??\:,\:{C};{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4} \\ $$$$\oint_{\:{C}} \:\frac{\mathrm{1}}{{z}}{e}^{{z}} \:\mathrm{d}{z},\:{C};\begin{cases}{{y}=\mathrm{1}\:,\:−\mathrm{1}\leq{x}\leq\mathrm{1}}\\{{y}=−\mathrm{1}\:,\:−\mathrm{1}\leq{x}\leq\mathrm{1}}\\{{x}=\mathrm{1}\:,\:−\mathrm{1}\leq{y}\leq\mathrm{1}}\\{{x}=−\mathrm{1}\:,\:−\mathrm{1}\leq{y}\leq\mathrm{1}}\end{cases}\: \\ $$

Question Number 220770 Answers: 1 Comments: 0

∫_0 ^( (π/2)) (( sin(x))/( (√(1 +(√(sin(2x)))))))dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{sin}\left({x}\right)}{\:\sqrt{\mathrm{1}\:+\sqrt{{sin}\left(\mathrm{2}{x}\right)}}}{dx}\: \\ $$

Question Number 220769 Answers: 2 Comments: 0

Question Number 220764 Answers: 1 Comments: 0

L= lim _( n→∞) (Σ_(k=1) ^n (k/(n^2 +k^2 ))).(∫^( 1) _( 0) e^(−x^2 ) dx)^(−1) .(Σ_(m=0) ^∞ (((−1)^m )/((2m+1)3^m )))

$$ \\ $$$$\:\:\boldsymbol{\mathrm{L}}=\:\boldsymbol{\mathrm{lim}}\underset{\:\boldsymbol{{n}}\rightarrow\infty} {\:}\left(\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\:\frac{\boldsymbol{{k}}}{\boldsymbol{{n}}^{\mathrm{2}} +\boldsymbol{{k}}^{\mathrm{2}} }\right).\left(\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } \boldsymbol{{dx}}\overset{−\mathrm{1}} {\right)}.\left(\underset{\boldsymbol{{m}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{m}}} }{\left(\mathrm{2}\boldsymbol{{m}}+\mathrm{1}\right)\mathrm{3}^{\boldsymbol{{m}}} }\right)\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 220755 Answers: 0 Comments: 0

Hmm....i need a help... generalize L_z ^(−1) {(1/(z^n +1))}= ∮_( C) (e^(zt) /(z^n +1)) dz

$$ \\ $$$$\mathrm{Hmm}....\mathrm{i}\:\mathrm{need}\:\mathrm{a}\:\mathrm{help}... \\ $$$$\mathrm{generalize}\: \\ $$$$\mathcal{L}_{{z}} ^{−\mathrm{1}} \left\{\frac{\mathrm{1}}{{z}^{{n}} +\mathrm{1}}\right\}=\:\oint_{\:{C}} \:\:\frac{{e}^{{zt}} }{{z}^{{n}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$

Question Number 220745 Answers: 3 Comments: 0

Question Number 220744 Answers: 1 Comments: 0

Question Number 220743 Answers: 1 Comments: 0

Question Number 220741 Answers: 1 Comments: 0

Question Number 220740 Answers: 1 Comments: 0

Question Number 220739 Answers: 1 Comments: 0

Question Number 220738 Answers: 1 Comments: 0

Question Number 220737 Answers: 2 Comments: 0

Question Number 220730 Answers: 2 Comments: 0

∫_0 ^( 1) (1/( (√(x(1 − x)(1 + kx))))) dx , (−1 < k < 1)

$$ \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{x}\left(\mathrm{1}\:−\:{x}\right)\left(\mathrm{1}\:+\:{kx}\right)}}\:{dx}\:,\:\left(−\mathrm{1}\:<\:{k}\:<\:\mathrm{1}\right)\:\:\: \\ $$$$ \\ $$

Question Number 220726 Answers: 0 Comments: 4

Question Number 220715 Answers: 2 Comments: 1

Question Number 220712 Answers: 0 Comments: 0

prove: ((2 tan 2A + tan A)/(4 tan 3A − tan 2A)) = sin^2 A

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\frac{\mathrm{2}\:{tan}\:\mathrm{2}{A}\:+\:{tan}\:{A}}{\mathrm{4}\:{tan}\:\mathrm{3}{A}\:−\:{tan}\:\mathrm{2}{A}}\:=\:{sin}^{\mathrm{2}} \:{A} \\ $$$$\: \\ $$

Question Number 220707 Answers: 2 Comments: 0

∫_(−∞) ^(+∞) ((x(tan^(−1) x)^3 )/((x^2 +1)^2 (1+e^(4tan^(−1) x) )))dx=?

$$\underset{−\infty} {\overset{+\infty} {\int}}\frac{{x}\left(\mathrm{tan}^{−\mathrm{1}} \:{x}\right)^{\mathrm{3}} }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{1}+\mathrm{e}^{\mathrm{4tan}^{−\mathrm{1}} \:{x}} \right)}{dx}=? \\ $$

Question Number 220706 Answers: 0 Comments: 0

Question Number 220704 Answers: 0 Comments: 0

Question Number 220700 Answers: 1 Comments: 0

Question Number 220694 Answers: 1 Comments: 1

Question Number 220693 Answers: 3 Comments: 2

Question Number 220677 Answers: 1 Comments: 0

∫(√(x+(√(x^2 +1 ))))dx

$$\int\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}\:}}{dx} \\ $$

Question Number 220676 Answers: 1 Comments: 0

∫ ((xdx)/((1−cosx)^2 ))

$$\int\:\frac{{xdx}}{\left(\mathrm{1}−{cosx}\right)^{\mathrm{2}} } \\ $$

Question Number 220674 Answers: 1 Comments: 0

∫∫∫_( E ) (z^2 /( (√(x^2 + y^2 )))) dV with the boundaries of the integration region E defined by; • x^2 + y^2 + z^2 ≤ 4 • x^2 + y^2 ≥ 1 • z ≥ 0

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\int\int_{\:{E}\:} \:\:\frac{{z}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} }}\:\:{dV} \\ $$$$\:\:\:\:\:\mathrm{with}\:\mathrm{the}\:\mathrm{boundaries}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integration}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{region}\:{E}\:\mathrm{defined}\:\mathrm{by};\: \\ $$$$\:\:\:\:\:\:\bullet\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} +\:{z}^{\mathrm{2}} \:\leqslant\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\bullet\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:\geqslant\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\bullet\:{z}\:\geqslant\:\mathrm{0} \\ $$$$ \\ $$

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