- #1
- 1,752
- 143
I get the right answer, but...
[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?
[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?