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Business Calculus
5. Integrals
5.3 Definite integral
Definite integral
What You'll Learn
Interpret definite integrals as the area under a curve between two limits
Calculate areas using geometric shapes like triangles, rectangles, trapezoids, and semicircles
Recognize that regions below the x-axis yield negative area values
Apply area formulas to evaluate integrals without using antiderivatives
Combine multiple regions to find total area across an interval
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
Skills
Definite Integrals
Area Under Curve
Geometric Interpretation
Integration Limits
Negative Area
Triangles
Semicircles
Trapezoids
