Скачать или смотреть Calculus 1 — 27.2: Area Between Two Curves

Learn how to compute the area between two curves using definite integrals — both when the bounds are given and when you must find them yourself. Two fully worked examples walk through the complete process, yielding exact answers of 10 and 125/6.

Key concepts covered:
• The core formula: integral from a to b of (top minus bottom) dx
• Identifying which function is on top across an interval
• Why parentheses around the bottom function are non-negotiable (sign distribution errors)
• Example 1: Area between y = 2x + 5 and y = x³ on [0, 2] with given bounds
• Example 2: Area between y = x² and y = x + 6 with unknown bounds
• Finding intersection points by setting the two functions equal and solving
• Using a test point between bounds to determine which curve is on top
• Term-by-term antidifferentiation and careful evaluation at both limits
• Handling fractions with common denominators in the final arithmetic
• What a negative result means and how to fix it (flip the subtraction order)
• Practice challenge: area between y = x² and y = 4 (answer: 32/3)

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SOURCE MATERIALS
The source materials for this video are from    • Calculus 1 Lecture 5.1:  Finding Area Betw...