Summary - Mathematics

.
Chapter 7 STD 12 Date : 16/12/25
Integration Maths
//X Section A
• Write the answer of the following questions. [Each carries 2 Marks] [32]

ò1 +
dx
1. Find x
1
6.3)
2. Find the following integrals : ò 1 + tan x dx
cos x
3. Integrate the rational functions :
(1 – sin x )(2 – sin x )

(Hint : Put, sin x = t)
1
4. Integrate the functions :
8 + 3x – x 2
dx
5. Obtain ò ex –1
6. Integrate the functions : 1 – 4x 2
tan 4( x ) sec2( x )
7. Obtain ò x
dx

sec2 x
8. Integrate the functions :
tan2 x + 4

x æ 1 + sin x ö
Integrate the functions in Exercises : e ç
è (1 + cos x ) ÷ø
9.

1
10.
Integrate the functions : (x – 1) ( x – 2 )

ò
dx
11. Evaluate the following :
1 + cos x
3x
12. Integrate the functions :
1 + 2x 4
cos2 x – cos 2a
13. Find the integrals of the function :
cosx – cosa
cos 2 x
14. Find the integrals of the function : (cos x + sin x )2
( x – 3)e x
15. Integrate the functions in Exercises :
( x – 1)3
16. Integrate the functions in Exercises : e2x sin x

//X Section B
• Write the answer of the following questions. [Each carries 4 Marks]
p
[64]
4
17. By using the propertie of definite integral evaluate the integrals in : ò log (1 + tan x ) dx
0
p
2
18. Evaluate ò log (sin x ) dx . X
0

é 1 ù
19. Find ò êê log (log x ) + (log x )2 úú dx .
ë û

, p
2
20. By using the propertie of definite integral evaluate the integrals in : ò (2 log sin x – log sin 2 x ) dx
0
5x + 3
21. Obtain ò 2
dx
x + 4 x + 10

x 2 + 1 élog( x 2 + 1) – 2log x ù
22. Integrate the function : ë û
x4
5x
23. Integrate the function :
( x + 1) ( x 2 + 9)
kp
24. Obtain
ò 3
tan x dx (Where, x ¹ 2 , k Î z)

–1 1– x
25. Integrate the function : tan 1+ x
p
x dx
26. Evaluate ò a cos x + b 2 sin 2 x
2 2
.
0
3
2
27. Evaluate ò | x sin ( px )| dx.
-1

28. Find ò( cot x + )
tan x dx.

x4
29. Find ò (x - 1)( x 2 + 1)
dx .

p
30. By using the propertie of definite integral evaluate the integrals in : ò log(1 + cos x ) dx
0

1– x
31. Integrate the function :
1+ x
p
2
cos2 x dx
32. Evaluate the definite integral : ò cos2 x + 4sin 2 x
0

, .
Chapter 7 STD 12 Date : 16/12/25
Integration Maths

Section [ A ] : 2 Marks Questions

No Ans Chap Sec Que Universal_QueId
1. - Chap 7 [Part-2] S17 7 QP25P11B1213_P2C7S17Q7
2. - Chap 7 [Part-2] S12 6.3 QP25P11B1213_P2C7S12Q6.3
3. - Chap 7 [Part-2] S5 17 QP25P11B1213_P2C7S5Q17
4. - Chap 7 [Part-2] S4 14 QP25P11B1213_P2C7S4Q14
5. - Chap 7 [Part-2] S17 6 QP25P11B1213_P2C7S17Q6
6. - Chap 7 [Part-2] S7 2 QP25P11B1213_P2C7S7Q2
7. - Chap 7 [Part-2] S17 4 QP25P11B1213_P2C7S17Q4
8. - Chap 7 [Part-2] S4 9 QP25P11B1213_P2C7S4Q9
9. - Chap 7 [Part-2] S6 18 QP25P11B1213_P2C7S6Q18
10. - Chap 7 [Part-2] S4 13 QP25P11B1213_P2C7S4Q13
11. - Chap 7 [Part-2] S13 6 QP25P11B1213_P2C7S13Q6
12. - Chap 7 [Part-2] S4 5 QP25P11B1213_P2C7S4Q5
13. - Chap 7 [Part-2] S3 13 QP25P11B1213_P2C7S3Q13
14. - Chap 7 [Part-2] S3 20 QP25P11B1213_P2C7S3Q20
15. - Chap 7 [Part-2] S6 20 QP25P11B1213_P2C7S6Q20
16. - Chap 7 [Part-2] S6 21 QP25P11B1213_P2C7S6Q21


Section [ B ] : 4 Marks Questions

No Ans Chap Sec Que Universal_QueId
17. - Chap 7 [Part-2] S10 8 QP25P11B1213_P2C7S10Q8
18. - Chap 7 [Part-2] S12 34 QP25P11B1213_P2C7S12Q34
19. - Chap 7 [Part-2] S12 38 QP25P11B1213_P2C7S12Q38
20. - Chap 7 [Part-2] S10 10 QP25P11B1213_P2C7S10Q10
21. - Chap 7 [Part-2] S17 11 QP25P11B1213_P2C7S17Q11
22. - Chap 7 [Part-2] S11 23 QP25P11B1213_P2C7S11Q23
23. - Chap 7 [Part-2] S11 6 QP25P11B1213_P2C7S11Q6
24. - Chap 7 [Part-2] S17 8 QP25P11B1213_P2C7S17Q8
25. - Chap 7 [Part-2] S11 22 QP25P11B1213_P2C7S11Q22
26. - Chap 7 [Part-2] S12 42 QP25P11B1213_P2C7S12Q42
27. - Chap 7 [Part-2] S12 41 QP25P11B1213_P2C7S12Q41
28. - Chap 7 [Part-2] S12 39 QP25P11B1213_P2C7S12Q39
29. - Chap 7 [Part-2] S12 37 QP25P11B1213_P2C7S12Q37

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