Applications of Definite Integrals

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Applications of Definite Integrals

• Dr. Ching I Chen

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7.1 Integral as Net Change (2, Example 1)Linear
Motion Revisited
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7.1 Integral as Net Change (3, Example
2-1)Linear Motion Revisited
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7.1 Integral as Net Change (4, Example
2-2)Linear Motion Revisited
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7.1 Integral as Net Change (5, Example
2-3)Linear Motion Revisited
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7.1 Integral as Net Change (6, Exploration
1-1)Linear Motion Revisited
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7.1 Integral as Net Change (7, Exploration
1-2)Linear Motion Revisited
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7.1 Integral as Net Change (8, Exploration
1-3)Linear Motion Revisited
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7.1 Integral as Net Change (9, Example 3)Linear
Motion Revisited
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7.1 Integral as Net Change (10)General Strategy
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7.1 Integral as Net Change (11)General Strategy
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7.1 Integral as Net Change (12, Example
4-1)General Strategy
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7.1 Integral as Net Change (13, Example
4-2)General Strategy
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7.1 Integral as Net Change (14, Example
4-3)General Strategy
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7.1 Integral as Net Change (15, Example
4-4)General Strategy
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7.1 Integral as Net Change (16, Example
4-5)General Strategy
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7.1 Integral as Net Change (17, Example
4-6)General Strategy
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7.1 Integral as Net Change (18, Example
5-1)Consumption over Time
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7.1 Integral as Net Change (19, Example
5-2)Consumption over Time
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7.1 Integral as Net Change (20, Example
5-3)Consumption over Time
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7.1 Integral as Net Change (21, Example 6)Net
Change from Data
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7.1 Integral as Net Change (22, Example 7) Work
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7.2 Areas in the Plane (1) Area Between Curves
How to find the area of a region that is bounded
above by one curve y f(x), and below by
another, y g(x)
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7.2 Areas in the Plane (2) Area Between Curves

• We partition the region into vertical strips of
  equal width
• Dx and approximate each strip with rectangle
  with base
• parallel to a, b. Each rectangle has

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7.2 Areas in the Plane (3) Area Between Curves
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7.2 Area in the Plane (4)Area Between Curves
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7.2 Areas in the Plane (5, Example 1) Area
Between Curves
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7.2 Areas in the Plane (6, Exploration 1-1,2)
Area Between Curves
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7.2 Areas in the Plane (7, Exploration 1-3) Area
Between Curves
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7.2 Areas in the Plane (8, Exploration 1-4,5)
Area Between Curves
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7.2 Areas in the Plane (9, Example 2) Area
Enclosed by Intersecting Curves
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7.2 Areas in the Plane (10, Example 3) Area
Enclosed by Intersecting Curves
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7.2 Areas in the Plane (11, Example 3) Area
Enclosed by Intersecting Curves
Solving by Matlab syms x fn 2cos(x)-xx1 intf
n int((fn), x, -1.2654, 1.2654) s1
double(intfn)
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7.2 Areas in the Plane (12, Example 4)
Boundaries with Changing Functions
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7.2 Areas in the Plane (13, Example 5)
Integrating with Respect to y
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7.2 Areas in the Plane (14, Example 5)
Integrating with Respect to y
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7.2 Areas in the Plane (15, Example 6)
Integrating with Respect to y
How about if the integrating with respect to x ?
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7.2 Areas in the Plane (16, Example 7) Saving
Time with Geometry Formulas
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7.3 Volumes (1) Volume as an Integral
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7.3 Volumes (2) Volume as an Integral
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7.3 Volumes (3) Volume as an Integral
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7.3 Volumes (4, Example 1) Volume as an Integral
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7.3 Volumes (5, Example 2) Square Cross Sections
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7.3 Volumes (6, Example 3) Circular Cross
Sections
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7.3 Volumes (7, Example 4) Circular Cross
Sections
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7.3 Volumes (8, Example 5-1) Circular Cross
Sections
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7.3 Volumes (9, Example 5-2) Circular Cross
Sections
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7.3 Volumes (10, Example 6) Other Cross Sections
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7.4 Lengths of Curves (1, Example 1-1) A Sine
Wave
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7.4 Lengths of Curves (2, Example 1-2) A Sine
Wave
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7.4 Lengths of Curves (3, Example 1-3) A Sine
Wave
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7.4 Lengths of Curves (4) Length of a Smooth
Curve
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7.4 Lengths of Curves (5) Length of a Smooth
Curve
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7.4 Lengths of Curves (6) Length of a Smooth
Curve
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7.4 Lengths of Curves (7) Length of a Smooth
Curve
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7.4 Lengths of Curves (8, Example 2) Length of a
Smooth Curve
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7.4 Lengths of Curves (9, Example 3) Vertical
Tangents, Corners, and Cusps
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7.4 Lengths of Curves (10, Example 4) Vertical
Tangents, Corners, and Cusps
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7.4 Lengths of Curves (11, Example 4) Vertical
Tangents, Corners, and Cusps
By Matlab syms x fn (1(2x3)2)0.5 intfn
int((fn), x, -4, 0) s1 double(intfn) fn
(1(2x-5)2)0.5 intfn int((fn), x, 0, 4) s2
double(intfn) L s1s2
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7.5 Applications from Science and Statistics (1)
Work Revisited (Example 1-1)
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7.5 Applications from Science and Statistics (2)
Work Revisited (Example 1-2)
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7.5 Applications from Science and Statistics (3)
Work Revisited (Example 1-3)
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7.5 Applications from Science and Statistics (4)
Work Revisited (Example 1-4)
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7.5 Applications from Science and Statistics (5)
Work Revisited (Example 2)
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7.5 Applications from Science and Statistics (6)
Fluid Force and Fluid Pressure
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7.5 Applications from Science and Statistics (7)
Fluid Force and Fluid Pressure (Example 3-a)
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7.5 Applications from Science and Statistics (8)
Fluid Force and Fluid Pressure (Example 3-b)
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7.5 Applications from Science and Statistics (9)
Normal Probabilities
omitted
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Normal Probabilities
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Normal Probabilities
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Normal Probabilities