# Riemann Sums 1

## Instructions

- Change the blue limit bar by changing the bottom slider
- Change the red limit bat by changing the top slider
- Change the number of "bars" that approximate the area under the curve with the right slider (bottom: none, top:many)

## Questions

- What function is the white line a graph of?

- If the white line is the graph of
*f(x)*, what is the estimate of
the area under the curve from *x*=0 to *x*=12 by using 12 boxes?

- If the white line is the graph of
*f(x)*, what is the estimate of
the area under the curve from *x*=0 to *x*=12 by using 24 boxes?

- If the white line is the graph of
*f(x)*, what is the estimate of
the area under the curve from *x*=0 to *x*=12 by using 100 boxes?

- If the white line is the graph of
*f(x)*, what is the estimate of
the area under the curve from *x*=-12 to *x*=0 by using 12 boxes?

- If the white line is the graph of
*f(x)*, what is the estimate of
the area under the curve from *x*=-12 to *x*=0 by using 24 boxes?

- If the white line is the graph of
*f(x)*, what is the estimate of
the area under the curve from *x*=-12 to *x*=0 by using 100 boxes?

- Which estimates were too big?

- Which estimates were too small?

- Predict if the estimate is too big or too small if we were to estimate
the area under the curve from
*x*=-12 to *x*=12 ( using 100 boxes)?

- Carry it out. Was your prediction correct?

- How would you write in symbolic form this integral (use your answer from number 1)?
##### Fr. Chris' java source is here