Lesson Notes By Weeks and Term v4 - SHS 2
PRINCIPLES OF CALCULUS
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PRINCIPLES OF CALCULUS
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Subject: Additional Mathematics
Class: SHS 2
Term: 2nd Term
Week: 13
Grade code: 2.3.1.LI.2
Strand code: 3
Sub-strand code: 1
Content standard code: 2.3.1.CS.2
Indicator code: 2.3.1.LI.2
Theme: CALCULUS
Subtheme: PRINCIPLES OF CALCULUS
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Welcome, future engineers, economists, and scientists! In our previous lessons, we learned to find the area of regular shapes like squares, circles, and triangles. But what happens when we encounter irregular shapes? Imagine a farmer in the Ashanti Region with a piece of land bordered by a straight road on one side and a winding river on the other. How can they calculate the exact area of their farm to know how much fertilizer to buy? This is where calculus comes to our aid. Today, we will learn a fundamental principle of calculus: approximating the area under a curve. We will learn to slice up these complex areas into simple rectangles that we *can* calculate.
Concept 1: The Problem of Irregular Area
Consider the curve of the function `y = x²` from `x = 0` to `x = 4`.
The shaded region is not a triangle, rectangle, or any standard shape we know. We cannot use a simple formula like `Area = length × width`. Our goal is to find the area of this shaded region. Concept 2: The Solution - Approximation with Rectangles
The core idea is simple: If we can't measure the curved area directly, let's fill it with shapes we *can* measure, like rectangles. We can approximate the area under the curve by drawing several thin rectangles and adding up their individual areas.