Presentation on theme: "Lesson 14.1. 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."— Presentation transcript:
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.
Although this is a good estimate, I can have a better estimate using more rectangles.
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.
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.
Now find the area of each of the rectangles! (remember – use midpoint to find the height)
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