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Use these properties of definite integrals:
[f(x) + g(x)]dx = f(x)dx + g(x)dx - k • f(x)dx = k f(x)dx
-
f(x)dx = 0 - f(x)dx = -
f(x)dx - f(x)dx +
f(x)dx = 
f(x)dx - If f(x) ≤ g(x) on [a, b], then f(x)dx ≤ g(x)dx
Remarks
Example 1: Given 
and 
, find 
, 
, and 
.
Example 2: Evaluate 
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
Cluster: Level 1: Recall
Cluster: Integral Calculus - Understand that integration is used to find areas, and evaluate integrals using rectangular approximations. From this, develop the idea that integration is the inverse operation to differentiation — the Fundamental Theorem of Calculus. Use this result to find definite and indefinite integrals, including using the method of integration by substitution. Apply approximate methods, such as the Trapezoidal Rule, to find definite integrals. Define integrals using Riemann sums, use the Fundamental Theorem of Calculus to find integrals using antiderivatives, and use basic properties of integrals. Integrate by substitution, and find approximate integrals.
Date Adopted or Revised: 02/14
Content Complexity Rating:
Level 1: Recall
-
More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Related Courses
This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
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