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AP Calculus AB

AP Calculus AB. Day 5 Section 4.2. Area Under a Curve. Find the area of the region bounded by y = f(x), the x-axis, x = a, and x = b. Approximate the area by creating rectangles of equal width whose endpoints are on f(x). n = # of rectangles. Each left endpoint is on f(x).

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AP Calculus AB

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  1. AP Calculus AB Day 5 Section 4.2 Perkins

  2. Area Under a Curve Find the area of the region bounded by y = f(x), the x-axis, x = a, and x = b. Approximate the area by creating rectangles of equal width whose endpoints are on f(x). n = # of rectangles Each left endpoint is on f(x) Each right endpoint is on f(x) This over-estimates the area under the curve… This under-estimates the area under the curve… We call it the Upper Sum. We call it the Lower Sum. Each method is called a Riemann Sum.

  3. How do we make these approximations for the area under a curve more accurate? Use more rectangles. (Always choose whichever sum involves right endpoints.) The Limit Definition for finding the area under a curve: or

  4. Find the area beneath (above the x-axis) in the interval [1,3]. a. Use 1 rectangle. b. Use 2 rectangles. If a specific number of rectangles is given, it is often easier to find the area without using sigma!

  5. Find the area beneath (above the x-axis) in the interval [1,3]. c. Use the limit definition.

  6. AP Calculus AB Day 5 Section 4.2 Perkins

  7. Area Under a Curve Find the area of the region bounded by y = f(x), the x-axis, x = a, and x = b. Approximate the area by creating rectangles of equal width whose endpoints are on f(x).

  8. How do we make these approximations for the area under a curve more accurate? The Limit Definition for finding the area under a curve:

  9. Find the area beneath (above the x-axis) in the interval [1,3]. a. Use 1 rectangle. b. Use 2 rectangles.

  10. Find the area beneath (above the x-axis) in the interval [1,3]. c. Use the limit definition.

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