Find the area of the smaller part of the circle x 2 + y 2 = a 2 cut off by the line

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 8. Application of Integrals

Subject: Maths - Class 12^th

Q. No. 7 of Exercise 8.1

Listen NCERT Audio Books - Kitabein Ab Bolengi

7

Find the area of the smaller part of the circle x² + y² = a² cut off by the line

It is given that the area of the smaller part of the circle cut off by the line

From the figure we can see that the area is ABCDA and it is shown by shaded region.

Now, we can observed that the area ABCD is symmetrical about x-axis.

Area ABCD = 2 × Area ABC

Area of ABC =

Therefore, required area is =

7

Chapter Exercises

Exercise 8.1

Exercise 8.2

Miscellaneous Exercise

1

Find the area of the region bounded by the curve y² = x and the lines x = 1, x = 4 and the x-axis in the first quadrant.

2

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

3

Find the area of the region bounded by x² = 4y, y = 2, y = 4 and the y-axis in the first quadrant.

4

Find the area of the region bounded by the ellipse

5

Find the area of the region bounded by the ellipse

6

Find the area of the region in the first quadrant enclosed by x-axis, line and the circle x² + y² = 4.

7

Find the area of the smaller part of the circle x² + y² = a² cut off by the line

8

The area between x = y² and x = 4 is divided into two equal parts by the line x = a, find the value of a.

9

Find the area of the region bounded by the parabola y = x² and y=|x|.

10

Find the area bounded by the curve x² = 4y and the line x = 4y – 2.

11

Find the area of the region bounded by the curve y² = 4x and the line x = 3.

12

Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is

13

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is