The defined integral below is, in fact, very hard to evaluate by common means.

I = ∫_o^π/2 √sin(x)/(√sin(x)+√cos(x)) dx

However, if you make the substitution x=(π/2-y), it becomes surprisingly easy to solve, by applying a basic concept of "defined integrals".

With this hint, can you, now, evaluate its value?

I=int(0 to ð/2 of sqrt sin(x)/sqrtsin(x)+sqrtcos(x))

Using the hint,

2I=int(0 to ð/2 of sqrt sin(x)+sqrt cos(x)/sqrt sin(x)+sqrt cos(x))

2I=ð/2

I=ð/4

PS:this is a common prob in my high school calculus textbook.Any 12th grader worth his/her salt should be able to do it.

Posted by Rex on 2005-06-26 14:02:46