Education Technology

### Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Calculus

# Bounded Areas

### Activity Overview

In this lesson, students will compare the Riemann Sum area estimates with the exact bounded area of a curve and the x-axis.

### Objectives

• Students will practice and discuss applications of finding the area bounded by a curve and the x-axis.
• Students will apply this information to finding the area bounded by two curves.
• Students will try to make a connection with how to understand these topics in both IB Mathematics and AP Calculus and on their final assessments.

### Vocabulary

 Riemann Sums Underestimate Overestimate Definite Integrals Bounded Areas Concavity

### About the Lesson

Students will use the subsequent pages of this TI-Nspire activity to refresh their skills on left-hand rectangle, right-hand rectangle, midpoint rectangle, and trapezoidal Riemann Sums given the bounded area between, the x-axis, and the vertical lines x = 1 and x = 3.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9545816779136658, "perplexity": 1880.4289911226474}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500288.69/warc/CC-MAIN-20230205193202-20230205223202-00456.warc.gz"}