Created on: September 11, 2014

Website Address: https://library.curriki.org/oer/Curriki-Calculus-Applications-of-Integrals

TABLE OF CONTENTS

- Applications of Integrals Table of Contents by Standard
- AI.1: Find specific antiderivatives using initial conditions.
- AI.2: Solve separable differential equations.
- AI.3: Solve differential equations of the form y' = ky.
- AI.4: Use definite integrals to find the area between a curve and the x-axis, or between two curves.
- AI.5: Use definite integrals to find the average value of a function over a closed interval.
- AI.6: Use definite integrals to find the volume of a solid with known cross-sectional area.
- AI.7: Use definite integrals to find the distance traveled by a particle along a line
- AI.8: Apply integration to model and solve real-world problems.

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).

Resources in this section listed by standard.

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.

Solve separable differential equations and use them in modeling real-world problems with and without technology.

Solve differential equations of the form y' = ky as applied to growth and decay problems.

Use definite integrals to find the area between a curve and the x-axis, or between two curves.

Use definite integrals to find the average value of a function over a closed interval.

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

Use definite integrals to find the distance traveled by a particle along a line

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.