CBSE Class 12 Mathematics Important Questions Chapter 8 – Application of Integrals
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.