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Overview
Calculus 120
Calculus
12. Determine the definite integral of a function
12.3 Definite integral
Definite Integral
Discover what a definite integral means, how it measures area under a curve, and how to evaluate it using the fundamental theorem of calculus.
What You'll Learn
Define the definite integral as the net signed area between a function and the x-axis over an interval.
Apply the fundamental theorem of calculus to evaluate integrals using antiderivatives.
Connect Riemann sums to the limit definition behind the definite integral.
Use properties such as additivity, linearity, and reversing limits to simplify integrals.
Evaluate definite integrals step by step with a worked numerical example.
Differentiate a definite integral with a variable limit using the appropriate rule.
What You'll Practice
1
Finding areas of trapezoids and rectangles under linear functions
2
Calculating semicircle and quarter-circle areas for curved regions
3
Evaluating integrals with regions above and below the x-axis
4
Sketching graphs and identifying geometric shapes to compute areas
5
Solving problems involving sums and differences of definite integrals
Why This Matters
Definite integrals are fundamental to calculus and appear everywhere from physics to economics. Understanding them geometrically builds your intuition for integration before tackling more complex techniques, making advanced calculus and real-world applications much more accessible.
Before You Start — Make Sure You Can:
This Unit Includes
10 Video lessons
Practice exercises
Learning resources
Skills
Definite Integrals
Area Under Curve
Geometric Interpretation
Integration Limits
Negative Area
Triangles
Semicircles
Trapezoids
NB Curriculum Aligned