Solution Found!
One of the earliest approximations to ? is . Verify that .
Chapter 4, Problem 81AE(choose chapter or problem)
\(\pi<\frac{22}{7}\) One of the earliest approximations to \(\pi\) is \(\frac{22}{7}\). Verify that \(0<\int_{0}^{1} \frac{x^{4}(1-x)^{4}}{1+x^{2}} d x=\frac{22}{7}-\pi\). Why can you conclude that \(\pi<\frac{22}{7}\) ?
Questions & Answers
QUESTION:
\(\pi<\frac{22}{7}\) One of the earliest approximations to \(\pi\) is \(\frac{22}{7}\). Verify that \(0<\int_{0}^{1} \frac{x^{4}(1-x)^{4}}{1+x^{2}} d x=\frac{22}{7}-\pi\). Why can you conclude that \(\pi<\frac{22}{7}\) ?
ANSWER:Problem 81AE
One of the earliest approximations to π is . Verify that . Why can you conclude that ?
Answer;
Step 1;
Now , we have to verify ; 0 < dx =
-
Consider …………(1)
, by using binomial distribution
can be written as ;
=
=
= .
=
=
= ) -
………(2)
=
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)dx
= ) -
dx
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dx
= - 4
+5
- 4
+4x - 4
=
- 4
+5
- 4
+4x - 4