tony873004

Science Advisor

Gold Member

- 1,749

- 141

[tex]

\int_{1/2}^{\sqrt 3 /2} {\frac{6}{{\sqrt {1 - t^2 } }}\,dt} [/tex]

[tex] F(x) = 6\,\sin ^{ - 1} x

[/tex]

[tex]

6\sin ^{ - 1} \frac{{\sqrt 3 }}{2} - 6\sin ^{ - 1} \frac{1}{2} = \pi [/tex]

I only know the answer is pi because I plugged it into my calculator and came out with 6.28... - 3.14... = 3.14...

Is there an easier way besides using the calculator to recognize that this equals pi?