Prove:

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 7. Integrals

Subject: Maths - Class 12^th

Q. No. 34 of Miscellaneous Exercise

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34

Prove:

Given:

Using partial differentiation:

⇒ 1 = Ax² +Ax+ B+Bx+ Cx²

⇒ 1 = B + (A+B)x + (A+C)x²

Equating the coefficients of x, x² and constant value. We get:

(a) B = 1

(b) A + B = 0 ⇒ A = -B ⇒ A = -1

( c) A + C =0 ⇒ C = -A ⇒ C = 1

Put these values in equation (1)

⇒ L.H.S = R.H.S

Hence proved.

34

Chapter Exercises

Exercise 7.2

Exercise 7.4

Exercise 7.5

Exercise 7.3

Exercise 7.1

Exercise 7.6

Exercise 7.8

Exercise 7.9

Exercise 7.10

Exercise 7.11

Exercise 7.7

Miscellaneous Exercise

1

Integrate the function:

2

Integrate the function:

3

Integrate the function:

4

Integrate the function:

5

Integrate the function:

6

Integrate the function:

7

Integrate the function:

8

Integrate the function:

9

Integrate the function:

10

Integrate the function:

11

Integrate the function:

12

Integrate the function:

13

Integrate the function:

14

Integrate the function:

15

Integrate the function:

16

Integrate the function:

17

Integrate the function:

18

Integrate the function:

19

Integrate the function:

20

Integrate the function:

21

Integrate the function:

22

Integrate the function:

23

Integrate the function:

24

Integrate:

25

Evaluate the definite integral:

26

Evaluate the definite integral:

27

Evaluate the definite integral:

28

Evaluate the definite integral:

29

Evaluate the definite integral:

30

Evaluate the definite integral:

31

Evaluate the definite integral:

32

Evaluate the definite integral:

33

Evaluate the definite integral:

34

Prove:

35

Prove:

36

Prove:

37

Prove:

38

Prove:

39

Prove:

40

Evaluate as a limit of a sum.

41

Choose the correct answers
is equal to

42

Choose the correct answers
is equal to

43

Choose the correct answers
If f (a + b – x) = f (x), then is equal to

44

Choose the correct answers
The value of