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AllQuestion and Answers: Page 27

Question Number 214622 Answers: 1 Comments: 0

Question Number 214618 Answers: 1 Comments: 0

∫_0 ^(Π/2) ((3(√(tan x)))/((sin x+cos x)^2 ))dx

$$\int_{\mathrm{0}} ^{\Pi/\mathrm{2}} \frac{\mathrm{3}\sqrt{\mathrm{tan}\:{x}}}{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} \:}{dx} \\ $$

Question Number 214603 Answers: 3 Comments: 0

Question Number 214601 Answers: 2 Comments: 0

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Question Number 214595 Answers: 0 Comments: 13

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Question Number 214587 Answers: 1 Comments: 0

Does Magnetic Monopole really not exist? In maxwell Equation ∫∫_( ∂V) B^→ ∙ da=0 ,B^→ is Magnetic field

$$\mathrm{Does}\:\mathrm{Magnetic}\:\mathrm{Monopole}\:\mathrm{really}\:\mathrm{not}\:\mathrm{exist}? \\ $$$$\mathrm{In}\:\mathrm{maxwell}\:\mathrm{Equation} \\ $$$$\int\int_{\:\partial{V}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{B}}}\centerdot\:\mathrm{d}\boldsymbol{\mathrm{a}}=\mathrm{0}\:\:,\overset{\rightarrow} {\boldsymbol{\mathrm{B}}}\:\mathrm{is}\:\mathrm{Magnetic}\:\mathrm{field} \\ $$

Question Number 214578 Answers: 1 Comments: 1

Question Number 214563 Answers: 0 Comments: 2

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Question Number 214536 Answers: 2 Comments: 4

Question Number 214556 Answers: 0 Comments: 4

Hey Tinku Tara, I got some plot issues. When I click the plot button, it displays the error message “Check if the variable name is x and you are logged in.”.

$$\mathrm{Hey}\:\mathrm{Tinku}\:\mathrm{Tara}, \\ $$$$\mathrm{I}\:\mathrm{got}\:\mathrm{some}\:\mathrm{plot}\:\mathrm{issues}. \\ $$$$\mathrm{When}\:\mathrm{I}\:\mathrm{click}\:\mathrm{the}\:\mathrm{plot}\:\mathrm{button},\:\mathrm{it}\:\mathrm{displays}\:\mathrm{the}\:\mathrm{error}\:\mathrm{message} \\ $$$$``\mathrm{Check}\:\mathrm{if}\:\mathrm{the}\:\mathrm{variable}\:\mathrm{name}\:\mathrm{is}\:{x}\:\mathrm{and}\:\mathrm{you}\:\mathrm{are}\:\mathrm{logged}\:\mathrm{in}.''. \\ $$

Question Number 214560 Answers: 1 Comments: 0

∫_1 ^( x) ((ln x)/( (√(1−(ln x)^2 ))))dx

$$\int_{\mathrm{1}} ^{\:\:{x}} \frac{\mathrm{ln}\:{x}}{\:\sqrt{\mathrm{1}−\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} }}{dx} \\ $$

Question Number 214514 Answers: 0 Comments: 7

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Question Number 214511 Answers: 0 Comments: 0

Let′s R(z) define as R(z)=((π ∫_0 ^( z) f^2 (t)dt)/(2π ∫_0 ^( z) f(t)(√(1+(f^((1)) (t))^2 ))dt)) and both integral ∫_0 ^( ∞) f^( 2) (t)dt , ∫_0 ^( ∞) f(t)(√(1+(f^((1)) (t))^2 ))dt =∞ lim_(z→∞) ((π ∫_0 ^( z) f^( 2) (t)dt)/(2π ∫_0 ^( z) f(t)(√(1+(f^((1)) (t))^2 ))dt)) =lim_(z→∞) ((π f(z))/(2π (√(1+(f^((1)) (z))^2 )))) ..??

$$\mathrm{Let}'\mathrm{s}\:{R}\left({z}\right)\:\mathrm{define}\:\mathrm{as}\: \\ $$$${R}\left({z}\right)=\frac{\pi\:\int_{\mathrm{0}} ^{\:{z}} \:{f}^{\mathrm{2}} \left({t}\right)\mathrm{d}{t}}{\mathrm{2}\pi\:\int_{\mathrm{0}} ^{\:{z}} \:{f}\left({t}\right)\sqrt{\mathrm{1}+\left({f}^{\left(\mathrm{1}\right)} \left({t}\right)\right)^{\mathrm{2}} }\mathrm{d}{t}} \\ $$$$\mathrm{and}\:\mathrm{both}\:\mathrm{integral} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:{f}^{\:\mathrm{2}} \left({t}\right)\mathrm{d}{t}\:,\:\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({t}\right)\sqrt{\mathrm{1}+\left({f}^{\left(\mathrm{1}\right)} \left({t}\right)\right)^{\mathrm{2}} }\mathrm{d}{t}\:=\infty \\ $$$$\underset{{z}\rightarrow\infty} {\mathrm{lim}}\:\frac{\pi\:\int_{\mathrm{0}} ^{\:{z}} {f}^{\:\mathrm{2}} \left({t}\right)\mathrm{d}{t}}{\mathrm{2}\pi\:\int_{\mathrm{0}} ^{\:{z}} \:{f}\left({t}\right)\sqrt{\mathrm{1}+\left({f}^{\left(\mathrm{1}\right)} \left({t}\right)\right)^{\mathrm{2}} }\mathrm{d}{t}} \\ $$$$=\underset{{z}\rightarrow\infty} {\mathrm{lim}}\:\frac{\pi\:{f}\left({z}\right)}{\mathrm{2}\pi\:\sqrt{\mathrm{1}+\left({f}^{\left(\mathrm{1}\right)} \left({z}\right)\right)^{\mathrm{2}} }}\:..?? \\ $$

Question Number 214509 Answers: 1 Comments: 4

Find the volume of the solid of revolution generated by rotating the area bounded by y=x(2−x) and y=x about the y−axis.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid}\:\mathrm{of}\:\mathrm{revolution} \\ $$$$\mathrm{generated}\:\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded} \\ $$$$\mathrm{by}\:{y}={x}\left(\mathrm{2}−{x}\right)\:\mathrm{and}\:{y}={x}\:\mathrm{about}\:\mathrm{the}\:\mathrm{y}−\mathrm{axis}. \\ $$

Question Number 214499 Answers: 3 Comments: 1

{ ((x^2 + (x + 3y) = 11)),((y^2 + (y + 3x) = 29)) :} ⇒ x + y = ?

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{x}\:\:+\:\:\mathrm{3y}\right)\:\:=\:\:\mathrm{11}}\\{\mathrm{y}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{y}\:\:+\:\:\mathrm{3x}\right)\:\:=\:\:\mathrm{29}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:? \\ $$

Question Number 214498 Answers: 1 Comments: 0

Question Number 214495 Answers: 0 Comments: 1

Question Number 214485 Answers: 1 Comments: 0

lim_(n→∞) ((1/(2∙4))+(1/(5∙7))+...+(1/((3n−1)(3n+1))))

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{7}}+...+\frac{\mathrm{1}}{\left(\mathrm{3}{n}−\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{1}\right)}\right) \\ $$

Question Number 214569 Answers: 2 Comments: 0

Question Number 214568 Answers: 1 Comments: 0

∫((b+ax)/(1+sin x)) dx

$$\int\frac{{b}+{ax}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx} \\ $$

Question Number 214566 Answers: 2 Comments: 0

somebody has posted following question and then deleted it again. { ((u_(n+1) =((4u_n −9)/(u_n −2)))),((u_0 =5)) :} find u_n =? (or something like this)

$${somebody}\:{has}\:{posted}\:{following} \\ $$$${question}\:{and}\:{then}\:{deleted}\:{it}\:{again}. \\ $$$$\begin{cases}{{u}_{{n}+\mathrm{1}} =\frac{\mathrm{4}{u}_{{n}} −\mathrm{9}}{{u}_{{n}} −\mathrm{2}}}\\{{u}_{\mathrm{0}} =\mathrm{5}}\end{cases} \\ $$$${find}\:{u}_{{n}} =?\:\left({or}\:{something}\:{like}\:{this}\right) \\ $$

Question Number 214483 Answers: 1 Comments: 0

Question Number 214479 Answers: 2 Comments: 0

Question Number 214471 Answers: 1 Comments: 0

d^2 −d+2=0 Σ_(k; d^2 −d+2=0) (1/k)=??

$${d}^{\mathrm{2}} −{d}+\mathrm{2}=\mathrm{0} \\ $$$$\underset{{k};\:{d}^{\mathrm{2}} −{d}+\mathrm{2}=\mathrm{0}} {\sum}\:\frac{\mathrm{1}}{{k}}=?? \\ $$

Question Number 214491 Answers: 0 Comments: 0

Question Number 214457 Answers: 2 Comments: 2

If (((x + 2y + 3z)^2 )/(x^2 + y^2 + z^2 )) = 14 find: ((x + y)/z) = ?

$$\mathrm{If}\:\:\:\frac{\left(\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{3z}\right)^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} }\:=\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\frac{\mathrm{x}\:+\:\mathrm{y}}{\mathrm{z}}\:=\:? \\ $$

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