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Lesson 14.1

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Just like a movie is a constantly moving figure, it can be broken into individual frames. I may not be able to find the area of this figure (created with the x-axis), but I can estimate it by breaking it into rectangles.

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Although this is a good estimate, I can have a better estimate using more rectangles.

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As x gets smaller, the my estimate gets more accurate. The integral is created by getting x (the length of each rectangle) as small as possible. Velocity-time curve: a graph in which x is the velocity and y is the time.

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A car accelerates from 0 to 60 ft/sec (41 mi/hour) in 8 seconds with a velocity after t seconds. Estimate how far the car travels in this time by dividing the interval 0 t 8 into 4 subintervals and using the midpoints of those intervals.

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Now find the area of each of the rectangles! (remember – use midpoint to find the height)

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Area: length * height Blue : 2 * f(1) General: 2 * f(1) + 2 *f(3) + 2 * f(5) + 2 f(7) 2 * 14.0625+ 2 *36.5625 + 2 * 51.5625+ 2 * 59.0625 322.5

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Calculate how far the car in Example 1 travels if the velocity is changed to 7.5t after t seconds. A = ½ bh A = ½ * 8 * 60 A = 240 feet (8, 60)

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2, 4, 5, 7, 8

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