In this, the fifth and last section of the course, the topics include:

Applications of integrals.
• Appropriate integrals are used in a variety of applications to model physical,
biological, or economic situations.  Although only a sampling of applications can be
included in any specific course, students should be able to adapt their knowledge
and techniques to solve other similar application problems. Whatever applications
are chosen, the emphasis is on using the method of setting up an approximating
Riemann sum and representing its limit as a definite integral.  To provide a common
foundation, specific applications should include finding the area of a region, the
volume of a solid with known cross sections, the average value of a function, the
distance traveled by a particle along a line, and accumulated change from a
rate of change.

Applications of antidifferentiation
• Finding specific antiderivatives using initial conditions, including applications to
motion along a line.
• Solving separable differential equations and using them in modeling
(including the study of the equation y’ =?ky and exponential growth).

## Collection Contents

by Janet Pinto

Resources in this section listed by standard.
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### AI.1: Find specific antiderivatives using initial conditions.

by Allen Wolmer

Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions, and applications to motion along a line.
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### AI.2: Solve separable differential equations.

by Allen Wolmer

Solve separable differential equations and use them in modeling real-world problems with and without technology.
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### AI.3: Solve differential equations of the form y' = ky.

by Allen Wolmer

Solve differential equations of the form y' = ky as applied to growth and decay problems.
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### AI.4: Use definite integrals to find the area between a curve and the x-axis, or between two curves.

by Allen Wolmer

Use definite integrals to find the area between a curve and the x-axis, or between two curves.
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### AI.5: Use definite integrals to find the average value of a function over a closed interval.

by Allen Wolmer

Use definite integrals to find the average value of a function over a closed interval.
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'C' - Curriki rating

### AI.6: Use definite integrals to find the volume of a solid with known cross-sectional area.

by Allen Wolmer

Use definite integrals to find the volume of a solid with known cross-sectional area.
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Curriki RatingC
'C' - Curriki rating

### AI.7: Use definite integrals to find the distance traveled by a particle along a line

by Allen Wolmer

Use definite integrals to find the distance traveled by a particle along a line
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Curriki RatingC
'C' - Curriki rating

### AI.8: Apply integration to model and solve real-world problems.

by Allen Wolmer

Apply integration to model and solve (with and without technology) real-world problems in physics, biology, economics, etc., using the integral as a rate of change to give accumulated change and using the method of setting up an approximating Riemann Sum and representing its limit as a definite integral.
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Curriki RatingC
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