CBSE Class 12 Maths Chapter-8 Important Questions – Free PDF Download
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CBSE Class 12 Mathematics Important Questions Chapter 8 – Application of Integrals
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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 + y2 = 4.
Ans.
x – axis
in first quadrant.
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) 2 + 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. 
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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. 
