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Question Number 46848 Answers: 0 Comments: 1

caculate ∫∫_D (x^2 −y^2 ) e^(−x^2 −y^2 ) dxdy with D ={(x,y)∈R^2 / x^2 +y^2 ≤4}

$${caculate}\:\:\int\int_{{D}} \:\:\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} } {dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{4}\right\} \\ $$

Question Number 46847 Answers: 0 Comments: 1

calculate ∫∫_(0≤x≤1 and 1≤y≤2) e^(x/y) dxdy

$${calculate}\:\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}} \:\:{e}^{\frac{{x}}{{y}}} {dxdy} \\ $$

Question Number 46846 Answers: 0 Comments: 1

calculate ∫∫_D ((x+y)/(√(1−x^2 −y^2 )))dxdy with D={(x,y)∈R^2 /x≥0,y≥0,x^2 +y^2 <1}

$${calculate}\:\int\int_{{D}} \:\:\:\:\frac{{x}+{y}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }}{dxdy}\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{0},{y}\geqslant\mathrm{0},{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} <\mathrm{1}\right\} \\ $$

Question Number 46845 Answers: 0 Comments: 0

calculate ∫_0 ^1 (e^(−x) /(1+x)) dx .

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{dx}\:. \\ $$

Question Number 46844 Answers: 0 Comments: 1

calculate ∫_0 ^∞ e^(−2t) ln(1+3t)dt

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{2}{t}} {ln}\left(\mathrm{1}+\mathrm{3}{t}\right){dt}\: \\ $$

Question Number 46843 Answers: 0 Comments: 0

let f(x)= ∫_0 ^x (t/(sin(t)))dt 1) find a explicit form of f(x) 2) calculate ∫_0 ^(π/2) (t/(sint))dt

$${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:\frac{{t}}{{sin}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{t}}{{sint}}{dt} \\ $$

Question Number 46842 Answers: 1 Comments: 1

find ∫ (dx/(x(√(x−x^2 ))))

$${find}\:\:\int\:\:\:\:\:\frac{{dx}}{{x}\sqrt{{x}−{x}^{\mathrm{2}} }} \\ $$

Question Number 46841 Answers: 1 Comments: 1

calculate ∫_(π/4) ^(π/3) (dx/(cosx sinx))

$${calculate}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\frac{{dx}}{{cosx}\:{sinx}} \\ $$

Question Number 46840 Answers: 0 Comments: 1

find lim_(n→+∞) Σ_(k=1) ^n ((n^(2 ) +k^2 )/(n^3 +k^3 ))

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{n}^{\mathrm{2}\:} +{k}^{\mathrm{2}} }{{n}^{\mathrm{3}} \:+{k}^{\mathrm{3}} } \\ $$

Question Number 46838 Answers: 1 Comments: 0

Question Number 46837 Answers: 0 Comments: 1

find∫(√(sin2x)) dx=??

$${find}\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$

Question Number 46833 Answers: 0 Comments: 1

Question Number 46831 Answers: 0 Comments: 0

Question Number 46829 Answers: 1 Comments: 0

Question Number 46827 Answers: 0 Comments: 0

Question Number 46821 Answers: 1 Comments: 0

Question Number 46816 Answers: 1 Comments: 0

Question Number 46814 Answers: 1 Comments: 0

Question Number 46813 Answers: 2 Comments: 1

Question Number 46809 Answers: 1 Comments: 0

an early question for the new year how many rectangular triangles with sides a, b, c ∈N^★ exist with one side =2019

$$\mathrm{an}\:\mathrm{early}\:\mathrm{question}\:\mathrm{for}\:\mathrm{the}\:\mathrm{new}\:\mathrm{year} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{rectangular}\:\mathrm{triangles}\:\mathrm{with}\:\mathrm{sides} \\ $$$${a},\:{b},\:{c}\:\in\mathbb{N}^{\bigstar} \:\mathrm{exist}\:\mathrm{with}\:\mathrm{one}\:\mathrm{side}\:=\mathrm{2019} \\ $$

Question Number 46805 Answers: 2 Comments: 0

In an A.p., the sum of first n terms is P , the sum of the next n terms is Q and the sum of further next n terms is R. Show that P, Q, R is an A.P.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{A}.\mathrm{p}.,\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{P}\:,\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{next}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{Q}\:\mathrm{and} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{further}\:\mathrm{next}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{R}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{P},\:\mathrm{Q},\:\mathrm{R}\:\mathrm{is}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}. \\ $$$$ \\ $$

Question Number 46802 Answers: 0 Comments: 1

Can someone please help me for the following: Solve fot x (exact value with formulas) : 17x^4 + 7x^3 − (√(11))x^2 − 18x + 3 = 0 Thank you

$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{for}\:\mathrm{the}\:\mathrm{following}: \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{fot}\:{x}\:\left(\mathrm{exact}\:\mathrm{value}\:\mathrm{with}\:\mathrm{formulas}\right)\:: \\ $$$$ \\ $$$$\mathrm{17}{x}^{\mathrm{4}} \:+\:\mathrm{7}{x}^{\mathrm{3}} \:−\:\sqrt{\mathrm{11}}\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{18}{x}\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 46790 Answers: 0 Comments: 4

Question Number 46760 Answers: 1 Comments: 1

how many natural solutions exist to x+y+z=11, x,y,z∈N

$${how}\:{many}\:{natural}\:{solutions}\:{exist} \\ $$$${to} \\ $$$${x}+{y}+{z}=\mathrm{11},\:{x},{y},{z}\in\mathbb{N} \\ $$

Question Number 46751 Answers: 0 Comments: 3

Prove that there exist 4 distinct positive integers such that each integer divides the sum of the remaining integers.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{4}\:\mathrm{distinct}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{each}\:\mathrm{integer}\:\mathrm{divides}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{remaining}\:\mathrm{integers}.\: \\ $$

Question Number 46748 Answers: 0 Comments: 0

∫(√(sin2x)) dx=??

$$\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$

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