[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?

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.

I'd look it up in a table of integrals, personally, though that may not be the non-calculator answer you were looking for...

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...

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.

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