Lesson Plan Math Class 12 (Ch-8) | Application of Integral

E-LESSON PLAN MATHEMATICS
CLASS-XII
CH-8 APPLICATION OF INTEGRAL

Lesson Plan Class 12th Subject Mathematics for Mathematics Teacher. Effective way of Teaching Mathematics. Top planning by the teacher for effective teaching in the class.

Rmb dav centnary public school Nawanshahr
NAME OF THE TEACHER				DINESH KUMAR
CLASS	10+2	CHAPTER	08	SUBJECT	MATHEMATICS
TOPIC	APPLICATION OF INTEGRAL			DURATION : 06 CLASS MEETINGS

TOPIC:

Chapter : 8 : Applications of Integrals

DURATION:

This chapter is divided into 4 modules and is completed in 10 class meetings.

PRE- REQUISITE KNOWLEDGE:

Knowledge of trigonometry Chapter 3 class 10+1,

Inverse trigonometry Chapter 2 class 10+2,

Indefinite Integration chapter 7 class 10+2

Definite Integral Chapter 7 Class 10+2

TEACHING AIDS:

Green Board, Chalk, Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:- Lecture method

LEARNING OBJECTIVES:

Applications in finding the area under simple curves, especially lines, circles, parabolas, ellipses (in standard form only).

The area between the lines and curves (the region should be clearly identified).

LEARNING OUTCOMES:

After studying this lesson students should know

the method drawing the graphs of line, circle, parabola, ellipse and hyperbola.

students should knows the method of finding the area between any two above said curves.

PROCEDURE :

Start the session by asking the questions related to the trigonometry, inverse trigonometry and formulas of Integration. Now introduce the topic application of Integral step by step as follows.

Topic
[Complete Explanation]

Introduction
In geometry, we have learnt formulas to calculate areas of various geometrical figures including triangles, rectangles, trapezium and circles. However they are inadequate for calculating the areas enclosed by curves.
Now we shall study a specific application of integrals to find the area under simple curves, area between lines and arcs of circles, parabola and ellipses.
First of all teacher should recapitulate the concept of drawing the graphs of straight line and other curves like Circle, Parabola, Ellipse and Hyperbola and make the students aware with their general equations.
Now teacher will introduce the topic to find the area under the simple curve like lines and circles, parabola and hyperbola.
Method of taking the limits:
If limit is taken on the x-axis, then find the value of y in terms of x. If limit is taken on the y- axis, then find the value of x in terms of y.
Algorithm to find the area under the curve
First of all find the limits on the x-axis or on the y-axis.
If limit is on the x-axis, then find the value of y in terms of x.
If limit is on the y-axis, then find the value of x in terms of y.
Find the area under the curve by integrating the given function in the respective limits.
We always take the absolute value of area. It means that area is always taken positive.
The formula which is mostly used in these questions
$\mathbf{\int\sqrt{a^{2}-x^{2}}dx=\frac{x}{2}\sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2}sin^{-1}\frac{x}{a}\$
Now teacher can provide some more problems to explore the knowledge of the student.

Example 1: [Q. No. 2 Exercise 8.1]

Find the are of the region bounded by y² = 9x, x = 2, x = 4 and the x- axis in the first quadrant.

Solution:

Given equation of the curve is

$\mathbf{y^{2}=9x\:\:\Rightarrow\:\:y=\sqrt{9x}=3\sqrt{x}$

Required area = Area of ABCD

$\mathbf{=\int_{2}^{4}ydx=\int_{2}^{4}3\sqrt{x}dx=3\int_{2}^{4}x^{\frac{1}{2}}dx$

$\mathbf{3\left[\frac{x^{3/2}}{3/2}\right]_{2}^{4}=3\times\frac{2}{3}\left[x^{3/2}\right]_{2}^{4}=2\left[4^{3/2}-2^{3/2}\right]$

$\mathbf{=2[8-\sqrt{8}]=[16-4\sqrt{2}]\;sq.units.$

STUDENTS DELIVERABLES:

Review questions given by the teacher.

Students should prepare the presentation in groups on the method of finding the area between any of the two curves.

Solve NCERT problems with examples.

EXTENDED LEARNING:-

Students can extend their learning in Mathematics through the RESOURCE CENTRE. Students can also find many interesting topics on mathematics at cbsemathematics.com

ASSESSMENT TECHNIQUES:

Assignment sheet will be given as home work at the end of the topic.

Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.

Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.

Re-test(s) will be conducted on the basis of the performance of the students in the test.

Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.

Puzzle

Quiz

Misconception check

Peer check

Students discussion

Competency Based Assessment link: M C Q

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