handout_11_20

# handout_11_20 - MATH 1A THE DEFINITE INTEGRAL 3 1...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 1A: THE DEFINITE INTEGRAL 3 1. Approximate the definite integral than or greater than the actual value? 0 (2 - x)dx using six rectangles and right endpoints. Is this value less Can you find the exact value of the integral? (Hint: What does the graph look like?) 2 2. Approximate the integral -2 4 - x2 dx (use your choice of the number of subintervals, left/ right endpoints or midpoints). What is the exact value of the integral? Date: November 20, 2009. 1 3. Use the definition of the definite integral (as a limit of the sum of areas of rectangles) to evaluate the following: 2 (x3 + 2x2 - x)dx. 0 The following identities may come in handy: n 1 + 2 + + n = i=1 n i= n(n + 1) . 2 n(n + 1)(2n + 1) . 6 n2 (n + 1)2 . 4 1 2 + 2 2 + + n2 = i=1 n i2 = i3 = i=1 1 3 + 2 3 + + n3 = 4. Find - sin(x)dx. (Hint: Before you venture into a computation, see if you can deduce anything graph- ically.) 1 1 5. What's bigger: 0 x3 dx or 1? What about 0 x3 dx and 1 ? 3 2 ...
View Full Document

## This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.

### Page1 / 2

handout_11_20 - MATH 1A THE DEFINITE INTEGRAL 3 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online