Mean Value Theorem (for definite integrals)
2
The average value of a function is the value that would give the same area if the function was a constant: 2 1 2 y x 3 2 0 1 2 A x dx 3 3 0 1 6 x 27 6 9 2 4.5 4.5 AverageV alue 1.5 3 A rea 1 A verageV alue W idth b a f x dx b a 1.5
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The average value of a function is the value that would give the same area if the function was a constant:. Mean Value Theorem (for definite integrals). If f is continuous on then at some point c in ,. - PowerPoint PPT Presentation
Transcript of Mean Value Theorem (for definite integrals)
The average value of a function is the value that would give the same area if the function was a constant:
21
2y x
3 2
0
1
2A x dx
33
0
1
6x
27
6
9
2 4.5
4.5Average Value 1.5
3
Area 1Average Value
Width
b
af x dx
b a
1.5
The mean value theorem for definite integrals says that for a continuous function, at some point on the interval the actual value will equal the average value.
Mean Value Theorem (for definite integrals)
If f is continuous on then at some point c in , ,a b ,a b
1
b
af c f x dx
b a
