Applications ofIntegrals class 12 cbse Previous year important questions

Application of Integrals

(2025)
1. The area of the region enclosed by the curve y = √x and the lines x = 0 and x
= 4 and x-axis is :
(1 Marks) (CBSE 2025 - 65/4/1)
A. 16/3 sq. units
B. 32/3 sq. units
C. 32/9 sq. units
D. 16/9 sq. units
2. The area of the region bounded by the curve y2 = x between x = 0 and x =
1 is :
(1 Marks) (CBSE 2025 - 65/6/1)
A. 2/3 sq units
B. 3/2 sq units
C. 3 sq units
D. 4/3 sq units
3. The area of the shaded region (figure) represented by the curves y = x2, 0 ≤
x ≤ 2 and y -axis is given by

, (1 Marks) (CBSE 2025 - 65/2/1)


A.


B.


C.


D.
4. The area of the region enclosed between the curve y = x|x|, x-axis, x =
−2 and x = 2 is :
(1 Marks) (CBSE 2025 - 65/5/1)
A. 8
B. 16/3
C. 8/3
D. 0
5. The area of the shaded region bounded by the curves y2 = x, x = 4 and the x-
axis is given by
(1 Marks) (CBSE 2025 - 65/1/1)

, A.


B.

C.


D.


6. Calculate the area of the region bounded by the curve and the
x -axis using integration.
(2 Marks) (CBSE 2025 - 65/4/1)
7. Sketch the graph of y = |x+3| and find the area of the region enclosed by the
curve, x-axis, between x = − 6 and x = 0, using integration.
(3 Marks) (CBSE 2025 - 65/1/1)
8. Draw a rough sketch for the curve y = 2 + |x+1|. Using integration, find the
area of the region bounded by the curve y = 2 + |x+1|, x = −4, x = 3 and y =
0.
(5 Marks) (CBSE 2025 - 65/6/1)
9. Using integration, find the area of the region bounded by the line y = 5x + 2,
the x - axis and the ordinates x = −2 and x = 2.