Riemann Sums Sec. 14-2 LEQ: HOW CAN YOU USE A RIEMANN SUM TO ESTIMATE THE AREA UNDER A CURVE?

Slides:

Advertisements

Similar presentations

Section 8.5 Riemann Sums and the Definite Integral.

Advertisements

A Riemann sum is a method for approximating the total area underneath a curve on a graph. This method is also known as taking an integral. There are 3.

Riemann Sums Jim Wang Mr. Brose Period 6. Approximate the Area under y = x² on [ 0,4 ] a)4 rectangles whose height is given using the left endpoint b)4.

Riemann Sums. Objectives Students will be able to Calculate the area under a graph using approximation with rectangles. Calculate the area under a graph.

1 Example 2 Estimate by the six Rectangle Rules using the regular partition P of the interval [0,  ] into 6 subintervals. Solution Observe that the function.

5.1 Estimating with Finite Sums Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2002 Greenfield Village, Michigan.

5.2 Definite Integrals Quick Review Quick Review Solutions.

Riemann Sums and the Definite Integral Lesson 5.3.

Definition: the definite integral of f from a to b is provided that this limit exists. If it does exist, we say that is f integrable on [a,b] Sec 5.2:

Lecture 19 – Numerical Integration 1 Area under curve led to Riemann sum which led to FTC. But not every function has a closed-form antiderivative.

A REA A PPROXIMATION 4-B. Exact Area Use geometric shapes such as rectangles, circles, trapezoids, triangles etc… rectangle triangle parallelogram.

1 5.e – The Definite Integral as a Limit of a Riemann Sum (Numerical Techniques for Evaluating Definite Integrals)

Chapter 6 The Definite Integral. § 6.1 Antidifferentiation.

Riemann Sums, Trapezoidal Rule, and Simpson’s Rule Haley Scruggs 1 st Period 3/7/11.

CHAPTER Continuity The Definite Integral animation  i=1 n f (x i * )  x f (x) xx Riemann Sum xi*xi* xixi x i+1.

In this section, we will investigate how to estimate the value of a definite integral when geometry fails us. We will also construct the formal definition.

5.1 Estimating with Finite Sums Greenfield Village, Michigan.

A REA A PPROXIMATION 4-E Riemann Sums. Exact Area Use geometric shapes such as rectangles, circles, trapezoids, triangles etc… rectangle triangle parallelogram.

Review Problems Integration 1. Find the instantaneous rate of change of the function at x = -2 _ 1.

Section 7.6 – Numerical Integration. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8.

Section 3.2 – Calculating Areas; Riemann Sums

Saving TI-83 List Data to a Program File. Saving TI-83 Lists to a Program Step 1: Create a New Program Press PRGM and arrow over to NEW Press ENTER and.

1 Example 1 Estimate by the six Rectangle Rules using the regular partition P of the interval [0,1] into 4 subintervals. Solution This definite integral.

Section 7.6 – Numerical Integration. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8.

Riemann Sums Lesson 14.2 Riemann Sums are used to approximate the area between a curve and the x-axis over an interval. Riemann sums divide the areas.

RIEMANN SUMS AP CALCULUS MS. BATTAGLIA. Find the area under the curve from x = 0 to x = 35. The graph of g consists of two straight lines and a semicircle.

To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3]  The area between the x-axis and the function Warm-up What is the area.

5.1 Approximating Area Thurs Feb 18 Do Now Evaluate the integral 1)

4.3 Riemann Sums and Definite Integrals. Objectives Understand the definition of a Riemann sum. Evaluate a definite integral using limits. Evaluate a.

Riemann Sums and the Definite Integral. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8.

Riemann Sums and Definite Integration y = 6 y = x ex: Estimate the area under the curve y = x from x = 0 to 3 using 3 subintervals and right endpoints,

Looking for insight in the special case of antiderivatives.

Chapter Definite Integrals Obj: find area using definite integrals.

Definite Integral df. f continuous function on [a,b]. Divide [a,b] into n equal subintervals of width Let be a sample point. Then the definite integral.

Riemann Sum. Formula Step 1 Step 2 Step 3 Riemann Sum.

5.1 Estimating with Finite Sums Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2002 Greenfield Village, Michigan.

LEQ: How do you evaluate logarithms with a base b? Logarithms to Bases Other Than 10 Sec. 9-7.

Clicker Question 1 What is ? (Hint: u-sub) – A. ln(x – 2) + C – B. x – x 2 + C – C. x + ln(x – 2) + C – D. x + 2 ln(x – 2) + C – E. 1 / (x – 2) 2 + C.

Definite Integrals & Riemann Sums

Announcements Topics: -sections 7.3 (definite integrals) and 7.4 (FTC) * Read these sections and study solved examples in your textbook! Work On: -Practice.

Lesson 5-2 The Definite Integral. Ice Breaker Find area between x-axis and y = 2x on [0,3] using 3 rectangles and right-end points v t Area of.

5.2 – The Definite Integral. Introduction Recall from the last section: Compute an area Try to find the distance traveled by an object.

The Definite Integral. Area below function in the interval. Divide [0,2] into 4 equal subintervals Left Rectangles.

[5-4] Riemann Sums and the Definition of Definite Integral Yiwei Gong Cathy Shin.

SECTION 4-3-B Area under the Curve. Def: The area under a curve bounded by f(x) and the x-axis and the lines x = a and x = b is given by Where and n is.

Finite Sums, Limits, and Definite Integrals.  html html.

5.1 Estimating with Finite Sums

Lecture 19 – Numerical Integration

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Riemann Sums and the Definite Integral

Riemann Sums as Estimates for Definite Integrals

Approximating Definite Integrals. Left Hand Riemann Sums.

Approximating Definite Integrals. Left Hand Riemann Sums.

Section 3.2 – Calculating Areas; Riemann Sums

Integration & Area Under a Curve

Limits of Riemann’s Sum

Sec 5.1: Areas and Distances

Saving TI-83 List Data to a Program File

Section 3.2 – Calculating Areas; Riemann Sums

§ 6.2 Areas and Riemann Sums.

Riemann Sums as Estimates for Definite Integrals

76 – Riemann Sums – Rectangles Day 2 – Tables Calculator Required

Approximation and Computing Area

5.1 Estimating with Finite Sums

AP Calculus December 1, 2016 Mrs. Agnew

Area Under a Curve Riemann Sums.

6.1 Estimating with Finite Sums

Jim Wang Mr. Brose Period 6

Sec 5.1: Areas and Distances

Presentation transcript:

Riemann Sums Sec LEQ: HOW CAN YOU USE A RIEMANN SUM TO ESTIMATE THE AREA UNDER A CURVE?

Riemann Sum

Riemann Sums on TI-83 & 84’s  Write a new program…name it Riemann  Enter the following lines in the program, pressing ENTER after each line  Press PRGM 4 to get “For”; press PRGM 7 to get “End”  : 0 sto S  : (B – A) / N sto H  : For(K, 1, N)  : A + (K – 1 + V) * H sto X  : S + Y 1 sto S  : End  : H * S

Test your program  Compute the left Riemann Sum for the f(x) = x 2 on the interval [2, 4] with 10 subintervals  Press QUIT to exit Prgm mode  Define Y 1 = x 2 in the equation editor  Assign the appropriate values  A (left endpoint of interval), B (right endpoint of interval), N (number of subintervals), V (type of sum; 0 for left,.5 for midpoint, 1 for right)  2 sto A  4 sto B  10 sto N  0 sto V  PRGM, EXEC, (Riemann)  ENTER…correct answer 17.48

Your Turn  LM 14-2 #1-3

Homework  Pgs #1-4, 10-17, 22, 23