# Homework Help: Approximating PI

1. Sep 29, 2009

Approximating PI Show that $$\int$$$$\stackrel{1}{0}$$$$\frac{x^{4}(1-x)^{4}}{1+x^{2}}$$dx=$$\frac{22}{7}$$-$$\Pi$$ Why does this imply that $$\Pi$$$$\triangleleft$$$$\frac{22}{7}$$

I have no clue where to begin with this, I'm at a loss, this is one of the questions for in my university project, first year. Any help is appreciated.

2. Sep 29, 2009

### aPhilosopher

Calculating the integral would probably be a good start.

What's the numerical value of the integral? Is it a big number or a small number? Is it positive or negative?

3. Sep 30, 2009

### Billy Bob

To evaluate $$\int_0^1 \frac{x^{4}(1-x)^{4}}{1+x^{2}}\,dx$$

multiply out the numerator, then use long division, then integrate from 0 to 1.

4. Sep 30, 2009

### HallsofIvy

Once you have done the integral and derived the result shown, if $\pi$ were greater than 22/7, the integral would be negative.

5. Sep 30, 2009

Now if I had to find the maximum of the numerator, how would I go about using it to show that $$\frac{22}{7}$$<$$\frac{\pi}{1024}$$<$$\frac{1}{100}$$ and how does it imply that the approximation $$\frac{22}{7}$$is accurate to 2 decimal places? I know that the $$\frac{1}{100}$$ would be used to imply that its accurate to 2 decimal places but how it does I'm not sure.