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NCERT Class 12 Maths Textbook Chapter 8 With Answer PDF Free Download
Chapter 8: Applications of Integrals
8.1 Introduction
In geometry, we have learned formulae to calculate areas of various geometrical figures including triangles, rectangles, trapeziums, and circles.
Such formulae are fundamental in the applications of mathematics to many real-life problems.
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.
In the previous chapter, we have studied to find the area bounded by the curve y = f (x), the ordinates x = a, x = b, and the x-axis, while calculating the definite integral as the limit of a sum.
Here, in this chapter, we shall study a specific application of integrals to find the area under simple curves, the area between lines and arcs of circles, parabolas, and ellipses (standard forms only). We shall also deal with finding the area bounded by the above-said curves.
8.3 Area between Two Curves
Intuitively, true in the sense of Leibnitz, integration is the act of calculating the area by cutting the region into a large number of small strips of the elementary area and then adding up these elementary areas.
Suppose we are given two curves represented by y = f (x), y = g (x), where f (x) ≥ g(x) in [a, b] as shown in Fig 8.13.
Here are the points of the intersection of these two curves given by x = a and x = b obtained by taking common values of y from the given equation of two curves.
| Author | NCERT |
| Language | English |
| No. of Pages | 20 |
| PDF Size | 629 KB |
| Category | Mathematics |
| Source/Credits | ncert.nic.in |
NCERT Solutions Class 12 Maths Chapter 8 Applications of Integrals
Question 1:
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
ANSWER:
The area of the region bounded by the curve, y2 = x, the lines, x = 1 and x = 4, and the x-axis is the area ABCD.
Question 2:
Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
ANSWER:
The area of the region bounded by the curve, y2 = 9x, x = 2, and x = 4, and the x-axis is the area ABCD.
Question 3:
Find the area of the region bounded by x2 = 4y, y = 2, y = 4, and the y-axis in the first quadrant.
ANSWER:
The area of the region bounded by the curve, x2 = 4y, y = 2, and y = 4, and the y-axis is the area ABCD.
NCERT Class 12 Maths Textbook Chapter 8 With Answer PDF Free Download