Smaller area enclosed by the circle x 2 + y 2 = 4 and the line x + y = 2 is

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 8. Application of Integrals

Subject: Maths - Class 12^th

Q. No. 6 of Exercise 8.2

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Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

The smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is shown by shaded region.

We can see that

Area ACBA = Area (OACBO) - Area (ΔOAB)

= (π – 2) units

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Chapter Exercises

Exercise 8.1

Exercise 8.2

Miscellaneous Exercise

1

Find the area of the circle 4x² + 4y² = 9 which is interior to the parabola x² = 4y.

2

Find the area bounded by curves (x – 1)² + y² = 1 and x² + y² = 1.

3

Find the area of the region bounded by the curves y = x² + 2, y = x, x = 0 and x = 3.

4

Using integration find the area of region bounded by the triangle whose vertices are (– 1, 0), (1, 3) and (3, 2).

5

Using integration find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.

6

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

7

Area lying between the curves y² = 4x and y = 2x is