P25 - 1 2 x 2 d x = Z 6 x 2-6 x d x = Z 6 x 2-6 x + 2 d x =...

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

View Full Document Right Arrow Icon
Project 25 MAC 2311 1. We continue to look at the parabolic arch formed by the function f ( x ) = 3 x - 1 2 x 2 on [ 0 , 6 ] . We would like to calculate its area using Riemann Sums of rectangles. Sketch the parabola below on [ 0 , 6 ] and shade the area beneath it. If we the interval [ 0 , 6 ] into n subintervals: Interval 1 , Interval 2 , . . . , Interval n , what is the width of each one? Show or explain why the right endpoint of Interval i is: 0 + i ± 6 n ² . If we approximate the area of the arch with n rectangles of equal width and by choosing x * i to be right endpoints, what is the area of the rectangle on Interval i (in terms of i and n )? What is the limit that represents the area of the arch? Area = lim n X i =1 Evaluate this limit using the technique learned in class (the formulas for sums of squares, cubes, etc. are in the notes or book).
Background image of page 1

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

View Full DocumentRight Arrow Icon
Evaluate these definite integrals using ONLY the previous answer and properties of integrals: Z 6 0 3 x -
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 2 x 2 d x = Z 6 x 2-6 x d x = Z 6 x 2-6 x + 2 d x = 2. If f ( x ) is negative on [ a, b ] , then R b a f ( x ) d x is negative. Why? Werent denite integrals dened to be areas? (Review your denitions.) Sketch the following piecewise-dened function, and evaluate the given denite integral in terms of area. Shade the regions whose areas you use to evaluate the denite integral. f ( x ) = 16-x 2 x 4-2 x < x < 3-2 x 3 Z 4-4 f ( x ) d x = Suppose that f ( x ) is the velocity (in m/s) of an object at time x in minutes. What is the total distance traveled by the object on [-4 , 2 ] ? Should Z 4 f ( x ) d x represent the total distance traveled by the object on [ 0 , 4 ] ? Think about what what a negative velocity means. . ....
View Full Document

Page1 / 2

P25 - 1 2 x 2 d x = Z 6 x 2-6 x d x = Z 6 x 2-6 x + 2 d x =...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online