1 of 5 INTEGRATION INTEGRALS and INTEGRATION. While you have been introduced to
ID: 1524645 • Letter: 1
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1 of 5 INTEGRATION INTEGRALS and INTEGRATION. While you have been introduced to the concept of a derivative, integrals will be new to you. READINGS on integration: Giancoli, 4 edition, pp. 39-40 and 169-170 An integral can be thought of as the OPPOSITE of a derivative, often called an ANTI derivative. For example, imagine you have the following two equations for the position of a truck and a car: Truck position: x 123m/s] t 50 meters Car position x00 123m/s] t 87 meters Both of these have the same horizontal velocity v. RECALL So for both vehicles ve 23 m/s The ONLY difference is that the truck is behind the car by (87-50)* 37 meters. IThey move together, but the truck remains 37 meters behind the car.) You can instead reverse the process to obtain the position as a function of time. This is called the INTEGRAL, or the ANTI-derivative: The velocity function is the Derivative of the position function v REVERSE above: The position function is the INTEGRAL of the velocity function: v dr C C? What's this? C is "some constant". RETURNING TO THE CAR AND TRUCK v, 23m/s (For BOTH the truck and car) And what about C? Well, for the car, C 87 meters, while for the truck C. 50 meters. THUS, for the truck's position: v alt C 23 m/sl dr 50meters 123 m/s] t 50metersExplanation / Answer
Q3.
area under the curve for 6 seconds=velocity*time
=22*6=192 meters
Q4. area under the curve=area of a triangle
=0.5*base*height
=0.5*5*20=50 m
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