CH 5.1(1).pdf - CHAPTER 5.1 Areas and distances How to find distance covered For constant velocity distance = velocity x time(in the meantime start

# CH 5.1(1).pdf - CHAPTER 5.1 Areas and distances How to find...

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CHAPTER 5.1 Areas and distances
How to find distance covered? For constant velocity, distance = velocity x time (in the meantime start thinking of something like length x width ) What about if the velocity is not constant?
Area under a continuous graph It is easy to find the areas if the lines are straight! ܣ ൌ ܣ ൅ ܣ ൅ ܣ ൅ ܣ The problem comes when we get a curved figure
We approximate the area of the region between and the -axis, on the interval by a sum of rectangles . How do find the area below but above the -axis?
A rectangle sum on the interval 1. First we choose the number of rectangles that we will use. Call that number . 2. Usually we make all the rectangles equally wide, so then the width of each rectangles is ௕ି௔ 3. The height of each rectangle is equal to the function value with being any point inside the rectangles base.
2 such rectangle sums ܮܵ ൌ ݂ ܽ Δݔ ൅ ݂ ݔ Δݔ ൅ ݂ ݔ Δݔ ൅ ݂ ݔ Δݔ ܴܵ ൌ ݂ ݔ Δݔ ൅ ݂ ݔ Δݔ ൅ ݂ ݔ Δݔ ൅ ݂ ܾ Δݔ ݊ ൌ 4 ⇒ Δݔ ൌ ܾ െ ܽ 4
Another left-hand sum Area

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• Spring '17
• J.S van Niekerk
• Binary relation, Left-handedness

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