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Apply knowledge about integrals to finding velocities from accelerations, solving separable differential equations, and finding areas and volumes. Apply integration to model, and solve problems in physics, biology, economics, etc. Find velocity functions and position functions from their derivatives, solve separable differential equations, and use definite integrals to find areas and volumes.

General Information

Number: MAFS.912.C.5

Title: Applications of Integration

Type: Cluster

Subject: Mathematics - Archived

Grade: 912

Domain-Subdomain: Calculus

Related Standards

This cluster includes the following benchmarks

Code	Description
MAFS.912.C.5.1:	Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions, and solving applications related to motion along a line.
MAFS.912.C.5.2:	Solve separable differential equations, and use them in modeling.
MAFS.912.C.5.3:	Solve differential equations of the form as applied to growth and decay problems.
MAFS.912.C.5.4:	Use slope fields to display a graphic representation of the solution to a differential equation, and locate particular solutions to the equation.
MAFS.912.C.5.5:	Use definite integrals to find the area between a curve and the x-axis or between two curves.
MAFS.912.C.5.6:	Use definite integrals to find the average value of a function over a closed interval.
MAFS.912.C.5.7:	Use definite integrals to find the volume of a solid with known cross-sectional area, including solids of revolution.
MAFS.912.C.5.8:	Apply integration to model, and solve problems in physical, biological, and social sciences.