# Important Questions for CBSE Class 12 Maths Chapter 8 - Application of Integrals

## CBSE Class 12 Maths Chapter-8 Important Questions – Free PDF Download

Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 8 – Application of Integrals prepared by expert Maths teachers from latest edition of CBSE(NCERT) books, On CoolGyan.Org to score more marks in CBSE board examination.

## 4 Mark Questions

1. Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and x – axis.
Ans. y2 = x is the equation of parabola and x = 1, x = 4 and x – axis
Req. area =

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

3. Find the area of the region bounded by the parabola y = x2 + 1 and the lines y = x,
x = 0 and x = 2.
Ans. y = x2 + 1
y = x, x = 0, x = 2

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

5. Find the area of the region bounded by the ellipse.

Ans.

6. Find the area of the region in the first quadrant enclosed by x – axis and by the circle x2 + y= 4.

Ans.
x – axis

7. Draw the graph of the curve and find the area bounded by this curve and the coordinate axis.
Ans.

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

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

10. Find the area of ellipse
Ans.

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

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

13. Find the area between the curve y = |x + 3|, the x – axis and the lines x = -6 and x = 0.
Ans.

14. Find the Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2.
Ans.

Area

15. Find the Area of the region bounded by the curve y2 = 4x, y – axis and the line y = 3.
Ans.

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

On solving (1) and (2)

17. Find the area of the region bounded by the parabolas y2 = 4ax and x2 = 4ay, a > 0.
Ans.

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

19. Find the area of the region
Ans.

20. Find the area bounded by the curves
Ans.

21. Find the area of the region:
Ans.

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

Ans.

On solving

23. Calculate the area of the region enclosed between eh circles:
x2 + y2 = 16 and (x + 4)2 + y2 =16.
Ans.

Intersecting at x = -2

24. Find the area of the circle x2 = y2 = 15 exterior to the parabola y2 = 6x
Ans.

25. Find the area bounded by the y – axis, y = cosx and y = sinx,
Ans.

26. Using integration, find the area of the region in the first quadrant enclosed by the
x – axis, the line y = x and the circle x2 + y2 = 32.
Ans.

## 6 Marks Questions

1. Find the area of the region bounded by the ellipse.
Ans.

Required area

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

3. Prove the area of a circle of radius r is square units.
Ans.

4. Find the area enclosed between the curve y = x3 and the line y = x.
Ans.

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

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

A (-1, 0) B (1, 3) C (3, 2)
Equation of AB

Similarly
Equation of BC
Equation of AC

7. Draw a rough sketch of the region and find the area enclosed by the region using method of integration.
Ans.

On solving

8. Using integration, find the area of the region given below: .
Ans.

9. Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.
Ans.

10. Find Smaller area enclosed by the circle x2 + y2 = 4 and the lines x + y = 2.
Ans.

Finding smaller area. On solving (1) and (2)

11. Find the area between the curves y = x and y = x2.
Ans.

On solving x = 0, 1

12. Sketch the graph of y = |x + 3| and evaluate
Ans.

13. Find the area bounded by the curve y = sinx between x = 0 and x = 2
Ans.

14. Find the area enclosed by the parabola y2 = 4ax and the line y = mx.
Ans.

15. Find the area of the region

Ans.

16. Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12.
Ans.

17. Find the area of the smaller region bounded by the ellipse and the line
Ans.

is the equation of ellipse and
is the equation of intercept form

18. Find the area of the smaller region bounded by the ellipse and the line
Ans.

19. Find the area of the region enclosed by the parabola x2 = y, the line y = x +2 and the x– axis.
Ans.

20. Using method of integration, find the area bounded by the curve |x| + |y| = 1.
Ans.

21. Find area bounded by curves
Ans.

22. Using method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3).

Ans.

23. Using method of integration, find the area of the region bounded by lines:
2x + y = 4, 3x – 2y = 6
and x – 3y + 5 = 0.
Ans.

24. Find the area of two regions
Ans.