{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ExamplesRiemannSum

# ExamplesRiemannSum - Example of Riemann Sums for f(x = x2...

This preview shows pages 1–3. Sign up to view the full content.

SubInterval [x i-1 , x i ] Sample Point Left Endpoint x i * = x i-1 Height of Rectangle i f(x i *) Length of Rectangle i Δx = x i-1 - x i Area of Rectangle i f(x i *) Δx [ 2, 5 ] x 1 * = 2 f(2) = 2 2 = 4 5 – 2 = 3 4 x 3 = 12 [ 5, 8 ] x 2 * = 5 f(5) = 5 2 = 25 8 – 5 = 3 25 x 3 = 75 [ 8, 11 ] x 3 * = 8 f(8) = 8 2 = 64 11 – 8 = 3 64 x 3 = 192 [ 11, 14 ] x 4 * = 11 f(11) = 11 2 = 121 14 – 11 = 3 121 x 3 = 363 TOTAL AREA = 642 Example of Riemann Sums for f(x) = x 2 on [2,14] with n = 4 subintervals with equal length given by (b-a)/n = (14 – 2)/4 = 3. Sample pts: Left Endpt b 14 4 a f(x)dx = 2 x 2 dx Σ i=1 f(x i *)Δx

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
SubInterval [x i-1 , x i ] Sample Point Right Endpt x i * = x i Height of Rectangle i f(x i *) Length of Rectangle i Δx = x i-1 - x i Area of Rectangle i f(x i *) Δx [ 2, 5 ] x 1 * = 5 f(5) = 5 2 = 25 5 – 2 = 3 25 x 3 = 75 [ 5, 8 ] x 2 * = 8 f(8) = 8 2 = 64 8 – 5 = 3 64 x 3 = 192 [ 8, 11 ] x 3 * = 11 f(11) = 11 2 = 121 11 – 8 = 3 121 x 3 = 363
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

ExamplesRiemannSum - Example of Riemann Sums for f(x = x2...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online