Integration — Area Under a Curve

\int_{x_1}^{x_2} y\, dx = 9

Exact area9.00

Riemann approximation5.91

Error3.094

a (curve shape)1

b (slant)0

c (vertical shift)0

x1 (lower bound)0

x2 (upper bound)3

Rectangles (n)4

With y = x², find the exact area from x = 0 to x = 3 — it should read 9
Set the rectangle count to 4 and see how far the approximation is from the exact value
Push the rectangle count high enough that the approximation lands within 0.1 of the exact area
With y = 2x + 1, find the exact area from x = 0 to x = 2 — it should read 6
Push the rectangle count to its maximum, and confirm the approximation error has dropped below 0.02