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7.3 - MATH1081 Monday,April11 Chapter7Section3...

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MATH 1081 Monday, April 11 Chapter 7 – Section 3 AREA AND THE DEFINITE INTEGRAL Homework #12 (due 4/18): Section 7.3 #8, 28, 36 Section 7.4 #4, 12, 26, 34, 56 Clicker Check-in: Choose any letter to check in now.
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Last week, we found the antiderivative of a function. That is, we “worked backwards” to figure out what function we would take the derivative of to yield a given function f x ( ) . Today, we will discuss a concept that is seemingly completely unrelated to the antiderivative. However, as we will see next time, in the Fundamental Theorem of Calculus , there is a very important connection between these to concepts.
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The basic question for today is: What is the area of the region between the curve f x ( ) and the x ‐axis from x = a to x = b ?
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Let’s begin by looking at the curve f x ( ) = 1 4 x 2 + 4 from x = 0 to x = 4 shown here.
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Let’s approximate the area of the region by using rectangles, for which we know how to find an area. For example, if we could use the 4 rectangles shown here.
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