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Chapter 5: Integration 5.4 The Fundamental Theorem of
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Mean Value Theorem for Definite Integrals
y =f(x) is a positive continuous faction over[a, b].
Geometrically, the Mean Value
Theorem says that there is a
number c in [a, b] such that the
rectangle with height equal to
the average value (c) of the
function and base width b-a has
exactly the same area as the
region beneath the graph of
from a to b.
The Mean Value Theorem for Definite Integrals asserts
(claims)
that this average value is alwaystaken on at least once by
the
function in the interval.
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Example
Solution
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Chapter 5: Integration 5.4 The Fundamental Theorem of
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Fundamental Theorem, Part 1
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Example
Solution
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Solution
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Example
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Example
Solution
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Example
Solution
The integral value = 0, but is the area under the curve is also
= 0?
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Solution
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Solution
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Chapter 5: Integration 5.4 The Fundamental Theorem of
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Solution
=
+
=
+
= , ,
=
+
+
=
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Solution
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Solution
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Because of symmetry about the y-axis ,
Solution
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Solve problems
1 to 46
Solution
The area of the rectanglebounded by the lines:
Rectangle area :
