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

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 8. Application of Integrals

Subject: Maths - Class 12^th

Q. No. 5 of Exercise 8.2

Listen NCERT Audio Books - Kitabein Ab Bolengi

5

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

The equation of the sides of the triangle are y = 2x + 1, y = 3x + 1 and x = 4.

So, solving above equations, we get the vertices of triangle are A (0, 1), B (4, 13) and c (4, 9).

We can see that Area (ΔACB) = Area (OLBAO) - Area (OLCAO)

= (24 + 4) – (16 + 4)

= 28 – 20

= 8 units.

Therefore, the required are is 8 units.

5

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