Average Value of a Function Over an Interval - Calculus

This calculus video tutorial explains how to find the average value of a function over a closed interval [a, b]. Examples include linear functions, quadratic functions, and square root functions. The average value formula can be derived from the mean value theorem formula for integrals. The average value represents the y coordinate of the point where the area under the curve is equal to the area of the rectangle formed at the point (c, f(c)) in the interval [a, b]. This video contains plenty of examples and practice problems on the average value theorem for integrals.

Applications of Integration - Free Formula Sheet:
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Antiderivatives:
   • Antiderivatives  

Fundamental Theorem - Part 1:
   • Fundamental Theorem of Calculus Part 1  

Fundamental Theorem - Part 2:
   • Fundamental Theorem of Calculus Part 2  

Net Change Theorem:
   • Net Change Theorem - Calculus Word Problems  

Mean Value Theorem - Integrals:
   • Mean Value Theorem For Integrals  

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Average Value of a Function:
   • Average Value of a Function Over an Interv...  

U-Substitution - Indefinite Integrals:
   • How To Integrate Using U-Substitution  

U-Substitution - Definite Integrals:
   • U-substitution With Definite Integrals  

1st Order Differential Equations:
   • Separable First Order Differential Equatio...  

Initial Value Problem:
   • Initial Value Problem  

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Area Between Two Curves:
   • Area Between Two Curves  

Disk and Washer Method:
   • Disk & Washer Method - Calculus  

Volume by the Shell Method:
   • Shell Method - Volume of Revolution  

Volume By Cross Sections:
   • Volumes Using Cross Sections - Calculus  

Arc Length Calculus Problems:
   • Arc Length Calculus Problems,  

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