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Question Number 100235 Answers: 0 Comments: 0

calculateΣ_(n=0) ^∞ (−1)^n ∫_1 ^e x^n lnx dx

$$\mathrm{calculate}\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\left(−\mathrm{1}\right)^{\mathrm{n}} \:\int_{\mathrm{1}} ^{\mathrm{e}} \:\mathrm{x}^{\mathrm{n}} \:\mathrm{lnx}\:\mathrm{dx} \\ $$

Question Number 100409 Answers: 0 Comments: 2

Question Number 100223 Answers: 1 Comments: 0

Question Number 100216 Answers: 1 Comments: 2

if I = ∫_0 ^(π/2) ((sin x)/(sin x + cos x))dx = ∫_0 ^(π/2) ((cos x)/(sin x +cos x))dx then I = ??

$$\mathrm{if}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}{dx}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{dx}\: \\ $$$$\mathrm{then}\:{I}\:=\:?? \\ $$

Question Number 100215 Answers: 2 Comments: 1

evaluate lim_(n→∞) ∫_1 ^e x^n ln x dx

$$\mathrm{evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{1}} ^{{e}} {x}^{{n}} \mathrm{ln}\:{x}\:{dx}\: \\ $$

Question Number 100207 Answers: 0 Comments: 2

Given an even fuction f(x) such that ∫_(−a) ^a f(x)dx = (√a) ∀a ≥0 find ∫_3 ^4 f(x) dx

$$\mathrm{Given}\:\mathrm{an}\:\mathrm{even}\:\mathrm{fuction}\:{f}\left({x}\right)\:\mathrm{such}\:\mathrm{that}\:\overset{{a}} {\int}_{−{a}} \:{f}\left({x}\right){dx}\:=\:\sqrt{{a}}\:\forall{a}\:\geqslant\mathrm{0} \\ $$$$\mathrm{find}\:\int_{\mathrm{3}} ^{\mathrm{4}} {f}\left({x}\right)\:{dx} \\ $$$$ \\ $$

Question Number 100198 Answers: 0 Comments: 1

Question Number 100197 Answers: 0 Comments: 0

Question Number 100193 Answers: 1 Comments: 3

(√(7+2(√(7−2(√(7+2(√(7−2(√(7+...)))))))))) ?

$$\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+...}}}}}\:? \\ $$

Question Number 100191 Answers: 1 Comments: 1

∫ x^2 e^x dx ?

$$\int\:{x}^{\mathrm{2}} \:{e}^{{x}} \:{dx}\:? \\ $$

Question Number 100190 Answers: 0 Comments: 0

∫_0 ^1 ((x^x /((1−x)^(1−x) ))−(((1−x)^(1−x) )/x^x ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{{x}^{{x}} }{\left(\mathrm{1}−{x}\right)^{\mathrm{1}−{x}} }−\frac{\left(\mathrm{1}−{x}\right)^{\mathrm{1}−{x}} }{{x}^{{x}} }\right){dx} \\ $$

Question Number 100189 Answers: 1 Comments: 0

∫tan^i xdx

$$\int{tan}^{{i}} {xdx} \\ $$

Question Number 100186 Answers: 0 Comments: 0

Question Number 100184 Answers: 1 Comments: 0

((ydx + xdy)/(1−x^2 y^2 )) + xdx = 0

$$\frac{\mathrm{ydx}\:+\:\mathrm{xdy}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} }\:+\:\mathrm{xdx}\:=\:\mathrm{0} \\ $$

Question Number 100179 Answers: 2 Comments: 0

Question Number 100178 Answers: 2 Comments: 0

what is the number of ordered pairs of positif integers (x,y) that satisfy x^2 +y^2 −xy=37

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ordered}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{positif}\: \\ $$$$\mathrm{integers}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{that}\:\mathrm{satisfy}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{xy}=\mathrm{37} \\ $$

Question Number 100173 Answers: 0 Comments: 2

Updated apk with the following changes (with fixes for all reported issues so far) is available at www.tinkutara.com. • Review a post • copy all to buffer • Ability to draw diagrams

$$\mathrm{Updated}\:\mathrm{apk}\:\mathrm{with}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{changes}\:\left(\mathrm{with}\:\mathrm{fixes}\:\mathrm{for}\:\mathrm{all}\:\mathrm{reported}\right. \\ $$$$\left.\mathrm{issues}\:\mathrm{so}\:\mathrm{far}\right)\:\mathrm{is}\:\mathrm{available}\:\mathrm{at} \\ $$$$\mathrm{www}.\mathrm{tinkutara}.\mathrm{com}. \\ $$$$\bullet\:\mathrm{Review}\:\mathrm{a}\:\mathrm{post} \\ $$$$\bullet\:\mathrm{copy}\:\mathrm{all}\:\mathrm{to}\:\mathrm{buffer} \\ $$$$\bullet\:\mathrm{Ability}\:\mathrm{to}\:\mathrm{draw}\:\mathrm{diagrams} \\ $$

Question Number 100343 Answers: 1 Comments: 3

l_(x→0) im ((f(x+1)^(1/x) )/(f(1))) f(1)=? help me

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{l}im}\:\frac{\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} }{\mathrm{f}\left(\mathrm{1}\right)}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{f}\left(\mathrm{1}\right)=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$

Question Number 100304 Answers: 0 Comments: 3

Question Number 100158 Answers: 1 Comments: 0

Question Number 100151 Answers: 0 Comments: 1

(√(lnx)) −ln(√x) =0 x=?

$$\sqrt{\mathrm{lnx}}\:−\mathrm{ln}\sqrt{\mathrm{x}}\:=\mathrm{0}\:\:\:\:\:\:\mathrm{x}=? \\ $$

Question Number 100150 Answers: 0 Comments: 3

x^(ln) −e^6 ∙x=0 x=? help me

$$\mathrm{x}^{\mathrm{ln}} −\mathrm{e}^{\mathrm{6}} \centerdot\mathrm{x}=\mathrm{0}\:\:\:\:\:\:\mathrm{x}=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$

Question Number 100341 Answers: 1 Comments: 1

An open box with a square base is to be made out of a given quantity of a cardboard of area c^2 square units.show the maximum volume of the box (c^2 /(6(√3))) cubic units

$$\mathrm{An}\:\mathrm{open}\:\mathrm{box}\:\mathrm{with}\:\mathrm{a}\:\mathrm{square} \\ $$$$\mathrm{base}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{made}\:\mathrm{out} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{given}\:\mathrm{quantity}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{cardboard}\:\mathrm{of}\:\mathrm{area}\:\mathrm{c}^{\mathrm{2}} \\ $$$$\mathrm{square}\:\mathrm{units}.\mathrm{show}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{box}\:\frac{\mathrm{c}^{\mathrm{2}} }{\mathrm{6}\sqrt{\mathrm{3}}}\:\:\mathrm{cubic}\:\mathrm{units} \\ $$$$ \\ $$

Question Number 100146 Answers: 1 Comments: 3

Question Number 100134 Answers: 1 Comments: 2

lim_(x→(π/2)) ((4sin x−(√(6(√(sin x))+10)))/((π/2)−x)) ?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{4sin}\:\mathrm{x}−\sqrt{\mathrm{6}\sqrt{\mathrm{sin}\:\mathrm{x}}+\mathrm{10}}}{\frac{\pi}{\mathrm{2}}−\mathrm{x}}\:? \\ $$

Question Number 100133 Answers: 1 Comments: 0

If sin^(−1) θ+sin^(−1) β=π θ+β−(2/(θ^2 +β^2 )) = ?

$$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \theta+\mathrm{sin}^{−\mathrm{1}} \beta=\pi\: \\ $$$$\theta+\beta−\frac{\mathrm{2}}{\theta^{\mathrm{2}} +\beta^{\mathrm{2}} }\:=\:? \\ $$

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