Exercise 9.8: Evaluation of a Bounded Plane Area by Integration

EXERCISE 9.8

1. Find the area of the region bounded by 3x âˆ’ 2 y + 6 = 0 , x = −3 , x = 1 and x-axis.

2. Find the area of the region bounded by 2x âˆ’ y +1 = 0 , y = −1, y = 3 and y-axis.

3. Find the area of the region bounded by the curve 2 + x âˆ’ x2 + y = 0 , x-axis, x = −3 and x = 3.

4. Find the area of the region bounded by the line y = 2x + 5 and the parabola y = x2 âˆ’ 2x .

5. Find the area of the region bounded between the curves y = sin x and y = cos x and the lines x = 0 and x = Ï€ .

6. Find the area of the region bounded by y = tan x , y = cot x and the lines x = 0 , x = Ï€/2 , y = 0.

7. Find the area of the region bounded by the parabola y 2 = x and the line y = x âˆ’ 2 .

8. Father of a family wishes to divide his square field bounded by x = 0 , x = 4 , y = 4 and y = 0 along the curve y2 = 4x and x2 = 4 y into three equal parts for his wife, daughter and son. Is it possible to divide? If so, find the area to be divided among them.

9. The curve y = ( x âˆ’ 2)2 +1 has a minimum point at P. A point Q on the curve is such that the slope of PQ is 2. Find the area bounded by the curve and the chord PQ.

10. Find the area of the region common to the circle x2 + y2 = 16 and the parabola y2 = 6x .

Answers:

1. 7.5

2. 2

3. 15

4. 36

5. 2√2

6. log 2

7. 9/2

8. yes, 16/3

9. 4/3

10. 4/3 ( 4π + √3)