The area between x = y 2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 8. Application of Integrals

Subject: Maths - Class 12^th

Q. No. 8 of Exercise 8.1

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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.

It is given that the area between x = y² and x = 4 is divided into two equal parts by the line x = a.

Thus, Area OAD = Area ABCD

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

⇒ Area OED = Area EFCD

Now, Area of OED =

Area of EFCD =

Therefore, from equations (1) and (2), we get,

Hence, the required value of a is .

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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