Summary - Mathematics

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Chapter 8 STD 12 Date : 16/12/25
Application of Integrals Maths
//X Section A
• Choose correct answer from the given options. [Each carries 2 Marks] [2]
1. The area of the region bounded by the circle x2 + y2 = 1 is ......... sq. unit.
(A) 2p (B) p (C) 3p (D) 4p

//X Section B
• Write the answer of the following questions. [Each carries 2 Marks] [30]
x2 y 2
1. Find the area of the region bounded by the ellipse + = 1.
4 9
0
2. Sketch the graph of y = |x + 2| and evaluate ò | x + 2 | dx.
-4
3. Find the area of the region bounded by the circle x2 + y2 = 16 using integration.
4. Find the area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = –1 and
x = 1.
5. Find the area of the region bounded by the ellipse 9x2 + 16y2 = 144.
0
6. Sketch the graph of y = | x + 3 | and evaluate
ò | x + 3 | dx.
–6
2 2
x y
7. Find the area enclosed by the ellipse 2
+
= 1.
a b2
8. Find the area bounded by the curve y = sin x between x = 0 and x = 2p.
9. Find the area enclosed by the circle x2 + y2 = a2.
x2 y 2
10. Find the area of the region bounded by the ellipse+ = 1.
16 9
11. ) Find the area under the given curves and given lines : y = x4; x = 1, x = 5 and X-axis
12. ) Find the area under the given curves and given lines : y = x2; x = 1, x = 2 and X-axis
p 3p
13.5) Find the area of the region bounded by the curve y = sin x, x = and x = .
2 2
14. Find the area bounded by the curve y = cos x between x = 0 and x = 2p.
15.1) Find the area of the region bounded by the y = x2 – 4, X-axis and the lines x = –1 and x = 2.

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Chapter 8 STD 12 Date : 16/12/25
Application of Integrals Maths

Section [ A ] : 2 Marks MCQ

No Ans Chap Sec Que Universal_QueId
1. B Chap 8 [Part-2] S4 12 QP25P11B1213_P2C8S4Q12


Section [ B ] : 2 Marks Questions

No Ans Chap Sec Que Universal_QueId
1. - Chap 8 [Part-2] S1 2 QP25P11B1213_P2C8S1Q2
2. - Chap 8 [Part-2] S8 12 QP25P11B1213_P2C8S8Q12
3. - Chap 8 [Part-2] S8 6 QP25P11B1213_P2C8S8Q6
4. - Chap 8 [Part-2] S3 3 QP25P11B1213_P2C8S3Q3
5. - Chap 8 [Part-2] S8 9 QP25P11B1213_P2C8S8Q9
6. - Chap 8 [Part-2] S2 2 QP25P11B1213_P2C8S2Q2
7. - Chap 8 [Part-2] S3 2 QP25P11B1213_P2C8S3Q2
8. - Chap 8 [Part-2] S2 3 QP25P11B1213_P2C8S2Q3
9. - Chap 8 [Part-2] S3 1 QP25P11B1213_P2C8S3Q1
10. - Chap 8 [Part-2] S1 1 QP25P11B1213_P2C8S1Q1
11. - Chap 8 [Part-2] S2 1.2 QP25P11B1213_P2C8S2Q1.2
12. - Chap 8 [Part-2] S2 1.1 QP25P11B1213_P2C8S2Q1.1
13. - Chap 8 [Part-2] S6 1.5 QP25P11B1213_P2C8S6Q1.5
14. - Chap 8 [Part-2] S3 4 QP25P11B1213_P2C8S3Q4
15. - Chap 8 [Part-2] S6 1.1 QP25P11B1213_P2C8S6Q1.1




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