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Evaluating Improper Integrals

Benjamin Wright

Benjamin Wright

6 min read

Study Guide Overview

This study guide covers improper integrals, focusing on evaluating definite integrals with infinite limits or unbounded functions. It explains how to express these integrals as limits, evaluate them using the First Fundamental Theorem of Calculus, and determine convergence or divergence. Examples and a walkthrough of a 2017 AP Calculus BC FRQ are provided.

Question 1 of 11

Which of the following integrals is considered an improper integral? ๐Ÿค”

โˆซ12x2dxโˆซ^2_1 x^2 dx

โˆซ05sin(x)dxโˆซ^5_0 sin(x) dx

โˆซ1โˆž1x2dxโˆซ^โˆž_1 \frac{1}{x^2} dx

โˆซ03eโˆ’xdxโˆซ^3_0 e^{-x} dx