Calculate improper integral $int_0^1 frac{ln x}{sqrt{1 - x^2}}dx$ [on hold]












-5














Calculate improper integral
$$
int_0^1 dfrac{ln x}{sqrt{1 - x^2}}dx
$$






integration







share|cite|improve this question















put on hold as off-topic by Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G

If this question can be reworded to fit the rules in the help center, please edit the question.













  • What are your thoughts on the problem ?
    – Digitalis
    18 hours ago






  • 1




    Maybe you could have searched a bit for past questions about this integral on this site. Some tips on searching: How to search on this site?
    – Martin Sleziak
    17 hours ago










  • You may exploit the substitution $x=sintheta$ and symmetry, or the substitution $x=sintheta$, Riemann sums and the identity $$prod_{k=1}^{n-1}sinleft(frac{pi k}{n}right)=frac{2n}{2^n}.$$ Differentiation of the Beta function is another way to go. This actually is about a single coefficient of the well-known Fourier series of $logsin$.
    – Jack D'Aurizio
    10 hours ago


















-5














Calculate improper integral
$$
int_0^1 dfrac{ln x}{sqrt{1 - x^2}}dx
$$






integration







share|cite|improve this question















put on hold as off-topic by Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G

If this question can be reworded to fit the rules in the help center, please edit the question.













  • What are your thoughts on the problem ?
    – Digitalis
    18 hours ago






  • 1




    Maybe you could have searched a bit for past questions about this integral on this site. Some tips on searching: How to search on this site?
    – Martin Sleziak
    17 hours ago










  • You may exploit the substitution $x=sintheta$ and symmetry, or the substitution $x=sintheta$, Riemann sums and the identity $$prod_{k=1}^{n-1}sinleft(frac{pi k}{n}right)=frac{2n}{2^n}.$$ Differentiation of the Beta function is another way to go. This actually is about a single coefficient of the well-known Fourier series of $logsin$.
    – Jack D'Aurizio
    10 hours ago
















-5












-5








-5







Calculate improper integral
$$
int_0^1 dfrac{ln x}{sqrt{1 - x^2}}dx
$$






integration







share|cite|improve this question















Calculate improper integral
$$
int_0^1 dfrac{ln x}{sqrt{1 - x^2}}dx
$$






integration




integration






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 18 hours ago









Did

246k23221455




246k23221455










asked 18 hours ago









vanminh85

964




964




put on hold as off-topic by Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G

If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Kavi Rama Murthy, Nosrati, Did, Shubham Johri, Elliot G

If this question can be reworded to fit the rules in the help center, please edit the question.












  • What are your thoughts on the problem ?
    – Digitalis
    18 hours ago






  • 1




    Maybe you could have searched a bit for past questions about this integral on this site. Some tips on searching: How to search on this site?
    – Martin Sleziak
    17 hours ago










  • You may exploit the substitution $x=sintheta$ and symmetry, or the substitution $x=sintheta$, Riemann sums and the identity $$prod_{k=1}^{n-1}sinleft(frac{pi k}{n}right)=frac{2n}{2^n}.$$ Differentiation of the Beta function is another way to go. This actually is about a single coefficient of the well-known Fourier series of $logsin$.
    – Jack D'Aurizio
    10 hours ago




















  • What are your thoughts on the problem ?
    – Digitalis
    18 hours ago






  • 1




    Maybe you could have searched a bit for past questions about this integral on this site. Some tips on searching: How to search on this site?
    – Martin Sleziak
    17 hours ago










  • You may exploit the substitution $x=sintheta$ and symmetry, or the substitution $x=sintheta$, Riemann sums and the identity $$prod_{k=1}^{n-1}sinleft(frac{pi k}{n}right)=frac{2n}{2^n}.$$ Differentiation of the Beta function is another way to go. This actually is about a single coefficient of the well-known Fourier series of $logsin$.
    – Jack D'Aurizio
    10 hours ago


















What are your thoughts on the problem ?
– Digitalis
18 hours ago




What are your thoughts on the problem ?
– Digitalis
18 hours ago




1




1




Maybe you could have searched a bit for past questions about this integral on this site. Some tips on searching: How to search on this site?
– Martin Sleziak
17 hours ago




Maybe you could have searched a bit for past questions about this integral on this site. Some tips on searching: How to search on this site?
– Martin Sleziak
17 hours ago












You may exploit the substitution $x=sintheta$ and symmetry, or the substitution $x=sintheta$, Riemann sums and the identity $$prod_{k=1}^{n-1}sinleft(frac{pi k}{n}right)=frac{2n}{2^n}.$$ Differentiation of the Beta function is another way to go. This actually is about a single coefficient of the well-known Fourier series of $logsin$.
– Jack D'Aurizio
10 hours ago






You may exploit the substitution $x=sintheta$ and symmetry, or the substitution $x=sintheta$, Riemann sums and the identity $$prod_{k=1}^{n-1}sinleft(frac{pi k}{n}right)=frac{2n}{2^n}.$$ Differentiation of the Beta function is another way to go. This actually is about a single coefficient of the well-known Fourier series of $logsin$.
– Jack D'Aurizio
10 hours ago












1 Answer
1






active

oldest

votes


















3














Hint:Use the substitution $x=sin theta.$ Then the integral will reduce to $$int_0^{pi/2} ln(sin theta)mathrm{d}theta.$$ Now use the property $$int_0^{a}f(x)mathrm{d}x=int_0^{a}f(a-x)mathrm{d}x. $$






share|cite|improve this answer




























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    3














    Hint:Use the substitution $x=sin theta.$ Then the integral will reduce to $$int_0^{pi/2} ln(sin theta)mathrm{d}theta.$$ Now use the property $$int_0^{a}f(x)mathrm{d}x=int_0^{a}f(a-x)mathrm{d}x. $$






    share|cite|improve this answer


























      3














      Hint:Use the substitution $x=sin theta.$ Then the integral will reduce to $$int_0^{pi/2} ln(sin theta)mathrm{d}theta.$$ Now use the property $$int_0^{a}f(x)mathrm{d}x=int_0^{a}f(a-x)mathrm{d}x. $$






      share|cite|improve this answer
























        3












        3








        3






        Hint:Use the substitution $x=sin theta.$ Then the integral will reduce to $$int_0^{pi/2} ln(sin theta)mathrm{d}theta.$$ Now use the property $$int_0^{a}f(x)mathrm{d}x=int_0^{a}f(a-x)mathrm{d}x. $$






        share|cite|improve this answer












        Hint:Use the substitution $x=sin theta.$ Then the integral will reduce to $$int_0^{pi/2} ln(sin theta)mathrm{d}theta.$$ Now use the property $$int_0^{a}f(x)mathrm{d}x=int_0^{a}f(a-x)mathrm{d}x. $$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 18 hours ago









        Thomas Shelby

        1,657216




        1,657216















            -

            Popular posts from this blog

            1300-talet

            Image
            Den här artikeln handlar om hundraårsperioden 1300–1399. För decenniet 1300–1309, se 1300-talet (decennium). .mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output ...
            Read more

            1300-talet

            Image
            Den här artikeln handlar om hundraårsperioden 1300–1399. För decenniet 1300–1309, se 1300-talet (decennium). .mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output ...
            Read more

            Display a custom attribute below product name in the front-end Magento 1.9.3.8

            Image
            0 I need to display a custom attribute bellow the product name and I don't know how can I call this attribute. I am editing the file /app/design/frontend/templatemela/MAG100219_1/template/catalog/product/view.phtml But how can I call this attribute in php? I tried calling a string echo with the name I put in the attribute, but it didn't work. Code is as below: <div class="page-title product-title"> <h1><?php echo $_helper->productAttribute($_product, $_product->getName(), 'name') ?></h1> </div> <div class="codigoinmetro"> <h2><?php echo $_helper->productAttribute($_product, $_product->getName(), 'registroinmetro') ?></h2> </div> php attrib...
            Read more