jackalknight Posted January 15, 2009 Share Posted January 15, 2009 [math] \int \frac{\sqrt{x}}{\sqrt{1-x}} dx [/math] From 0 to .5 How would you go about solving this without the use of a calculator? Link to comment Share on other sites More sharing options...
Klaynos Posted January 15, 2009 Share Posted January 15, 2009 Well can you think of a way to rewrite it to get rid of the fraction? And then I'd give by parts a go... Don't know whether it'd work or not mind. Link to comment Share on other sites More sharing options...
Bignose Posted January 15, 2009 Share Posted January 15, 2009 I'd look it up in a table of integrals, personally, though that may not be the non-calculator answer you were looking for... Link to comment Share on other sites More sharing options...
Klaynos Posted January 15, 2009 Share Posted January 15, 2009 I'd look it up in a table of integrals, personally, though that may not be the non-calculator answer you were looking for... That's what I'd do as well if I actually just wanted the answer There's no point in reinventing the wheel as long as you understand how the wheel works of course... Link to comment Share on other sites More sharing options...
kemal Posted May 20, 2009 Share Posted May 20, 2009 split it up within the intergral. I am pretty sure the 1/(that denominator) is an inverse trig derivative. I THINK inverse tan I could be wrong though. Link to comment Share on other sites More sharing options...
Jad2192 Posted May 21, 2009 Share Posted May 21, 2009 You could use a combination of u substitution (u^2 = x) and trig-substitution (u = sin(a)). I did it out by hand and got as final answer (pi-2)/4 Link to comment Share on other sites More sharing options...
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