NCERT Class 12-Mathematics: Chapter –8 Application of Integrals Part 1

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8.1 Overview

This chapter deals with a specific application of integrals to find the area under simple curves, area between lines and arcs of circles, parabolas and ellipses, and finding the area bounded by the above said curves.

8.1.1 The area of the region bounded by the curve , axis and the lines and is given by the formula:

8.1.2 The area of the region bounded by the curve axis and the lines is given by the formula:

8.1.3 The area of the region enclosed between two curves and the lines is given by the formula.

8.1.4 , then

8.2 Solved Examples

Short Answer (S.A)

Question 1:

Find the area of the curve between and .

Fig. 8.1-Find the area of the curve

Find the Area of the Curve

Answer:

Question 2:

Find the area of the region bounded by the curve , the axis and the lines and .

Fig-8.2.-Find the area of the region bounded by the curve

Find the Area of the Region Bounded by the Curve

Answer:

Question 3:

Find the area of the region bounded by the parabola and the straight line .

Fig.8.3-Find the area of the region bounded by the parabola

Find the Area of the Region Bounded by the Parabola

Answer:

The intersecting points of the given curves are obtained by solving the equations and for and .

We have which gives and .

Thus, the points of intersection are . Hence

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