Riemann Sums
Task 1
The area between the curves is approximated by slicing it into three rectangles. This is called a [b][url=https://en.wikipedia.org/wiki/Bernhard_Riemann]Riemann[/url] sum[/b].[br]On your paper, calculate the area of the rectangles to show that their sum matches the value of "left Riemann sum".
Task 2
How could you make a more accurate approximation? Do it, and compare your approximation to the exact area. Is it closer than the Riemann sum with 3 rectangles?
Area between curves
Task 1
Calculate the left Riemann sum and check that it agrees with the "Approximate Area".
Task 2
How does the height of the rectangles depend on the two functions f(x) and g(x)? Write a formula, then check your answer.
Task 3
Write a formula for calculating the area between any two curves f(x) and g(x) from x = a to x = b. Check your answer.