Area Under Simple Curve
Chapter Name : Application Of Integrals |
Sub Topic Code : 104_12_08_02_01 |
Topic Name : Area Under Simple Curve |
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Sub Topic Name : Area Under Simple Curve |
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Introduction
In geometry, we have learnt formulae to calculate areas of various geometrical figures including triangles, rectangles, trapeziums and circles. The formulae of elementary geometry allow us to calculate areas of many simple figures. However, they are inadequate for calculating the areas enclosed by curves. For that we shall need some concepts of Integral Calculus. We can apply concept of integrals to find the area under simple curves, area between lines and arcs of circles, parabolas and ellipses (standard forms only).
Pre-Requisites:
• Differentiation • Integration Basics • Area under a Curve using Integration • Areas of different shapes.
Activity:
Observe the different curved solids around you in school and at home. Think about how you can determine their area.
Real Life Question:
How do you find area of a ellipse or a parabola?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Integration | Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total. |
| Area | Area is a quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane. |
| Curved Surface | A curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. |
Learning aids / Gadgets
| Gadgets | How it can be used |
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Real life uses :
A ball thrown in the air travels in a parabolic fashion. If the path is drawn on a graph we will get a parabola whose area can be determined using integrals.
Practical examples around us
| Examples | Explainations |
|---|---|
| A ball in the air | A ball thrown in the air travels in a parabolic fashion. If the path is drawn on a graph we will get a parabola whose area can be determined using integrals. |
What you learn in Theory:
We learn how to find area of simple curves using Integral calculus.
What you learn in Practice:
We learn how to find the area of a parabola or a ellipse using Integrals.