+118723 
+118723 @@ End of Day Wrap Sat 20/6/15 Sydney, Australia Time 11:58pm ♪ ♫
Hello everyone 
Our wonderful answers were provided by Syllogist, HeatherF, MathsGod1, DarkBlaze347, CPhill, Zacismyname, radix, Sir-Emo-Chappington, Heureka and Alan. Thank you.
If you would like to comment on other site issues please do so on the Lantern Thread. Thank you.
Interest Posts:
1) Ratio Problem Continued Thanks Alan, CPhill and Civonamzuk
2) Trig integration Continued Thanks Syllogist, Melody. CPhill, Alan and Heureka
3) Trig integration2 Continued Thanks Heureka and Melody
4) Difficult fraction equation Thanks Radix, Melody Alan
5) Statistics - Confidence interval Thanks Alan
♫♪ ♪ ♫ ♬ ♬ MELODY ♬ ♬ ♫♪ ♪ ♫
+118723 Sun 21/6/15
If you would like to comment on other site issues please do so on the Lantern Thread. Thank you.
Interest Posts:
FTJ means 'For the juniors'
1) Interactive practice page for gradient FTJ Thanks Radix
2) Interactive practice for number plane coordinates Thanks Radix
3) Stacks of bricks FTJ Thanks Sir-Emo-Chappington
4) Calculus - Find maximum volume Melody
5) Trig proof (I am not sure what is wanted) Melody
6) Why is one answer discarded? Melody
7) Inequality and a new graphing program Thanks Sir-Emo-Chappington and Melody
8) Simplifying horrible algebraic fractions Melody
9) Multiple Choice - order of operation LOL Thanks Sir-Emo-Chappington, Alan and Melody
10) Trig equations in polar form 
Thanks Melody and Alan
♫♪ ♪ ♫ ♬ ♬ MELODY ♬ ♬ ♫♪ ♪ ♫
+118723 Thanks Heureka and Chris,
I really like Alan's solution here.
It is so elegant.
And, once placed in front of me, it is so 'obvious' LOL
What is the chances of it being obvious (to me) next time without Alan answering first.
Probably about 0.01
I am trying to think about how something like this can be used in this question.
http://web2.0calc.com/questions/integral_4
I have included both these questions into the "Great Answers to Learn from" sticky thread
+118723 I am considering the very elegant substitution that Alan used here
http://web2.0calc.com/questions/integrate-cos-1x-2-1-x-2-1-2
I am going to look for something like that here.
Heureka used a substitution but it looked hard to me. 
$$\\\int x\;\sqrt {0.25 - x^2} dx\\\\
Let \\
u=0.25-x^2\\\\
du=-2x\;dx\\\\
dx=\frac{du}{-2x}\\\\
so\\
\int x\;\sqrt {0.25 - x^2} dx\\\\
=\int \not{x}\;\sqrt {u}\; \frac{du}{-2\not{x}}\\\\
=\int \;\frac{u^{1/2}}{-2}\; du\\\\
=\frac{2u^{3/2}}{3*-2}+c\\\\
=\frac{-u^{3/2}}{3}+c\\\\
=\frac{-(0.25-x^2)^{3/2}}{3}+c\\\\$$
YES I Like that - thanks Alan
