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

1. What function is the white line a graph of?
   
   
2. 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?
   
   
3. 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?
   
   
4. 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?
   
   
5. 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?
   
   
6. 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?
   
   
7. 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?
   
   
8. Which estimates were too big?
   
   
9. Which estimates were too small?
   
   
10. 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)?
    
    
11. Carry it out. Was your prediction correct?
    
    
12. How would you write in symbolic form this integral (use your answer from number 1)?

    Fr. Chris' java source is here