Florida B.E.S.T. MA.912.C.5.5
The Standard
Find the area between a curve and the x-axis or between two curves by using definite integrals.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify intersection points and decide which graph is above the other across each interval. They set up and evaluate definite integrals, splitting intervals when needed, and report nonnegative areas in square units.
What Mastery Looks Like
- Given graphs or equations, a student finds the correct bounds and writes the upper function minus the lower function. The student splits intervals when needed, evaluates accurately, and checks that the result is reasonable and nonnegative.
Common Misconceptions
- Students may subtract in the wrong order or treat a negative definite integral as a negative area. They may also miss intersection points, use incorrect bounds, or fail to split an interval when the upper curve changes.
How to Assess It
- Exit ticket: Find the area enclosed by y = x and y = x² from x = 0 to x = 1. Show the bounds, integral, calculation, and units.
Lesson moves
Ways to Teach It
Give pairs printed graphs; students shade bounded regions, mark intersection points, cut vertical paper strips, and label each strip's height as top minus bottom.
Ask, “Why can a definite integral be negative while an area cannot?” Students write three sentences, then compare answers with a partner.
Run a card sort matching graphs, bounds, integrands, and numerical areas; include cards where curves cross and intervals must be split.
Model two changing production rates over time, then integrate their difference to find the total production gap during a shift.
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Printable MA.912.C.5.5 Worksheet
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Related Standards
- MA.912.C.5.6
Find the average value of a function over a closed interval by using definite integrals.
- MA.912.C.4.4
Evaluate definite integrals by using the Fundamental Theorem of Calculus.
- MA.912.C.5.7
Find the volume of a figure with known cross-sectional area, including figures of revolution, by using definite integrals.
- MA.912.C.4.6
Evaluate or solve problems using the properties of definite integrals.
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