NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.5 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.5.
- Integrals Class 12 Ex 7.1
- Integrals Class 12 Ex 7.2
- Integrals Class 12 Ex 7.3
- Integrals Class 12 Ex 7.4
- Integrals Class 12 Ex 7.6
- Integrals Class 12 Ex 7.7
- Integrals Class 12 Ex 7.8
- Integrals Class 12 Ex 7.9
- Integrals Class 12 Ex 7.10
- Integrals Class 12 Ex 7.11
Board | CBSE |
Textbook | NCERT |
Class | Class 12 |
Subject | Maths |
Chapter | Chapter 7 |
Chapter Name | Integrals |
Exercise | Ex 7.5 |
Number of Questions Solved | 23 |
Category | NCERT Solutions |
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.5
Integrate the rational function in exercises 1 to 21
Ex 7.5 Class 12 Maths Question 1.
Solution:
let ≡
⇒ x ≡ A(x+2)+B(x+1)….(i)
putting x = -1 & x = -2 in (i)
we get A = 1,B = 2
=-log|x+1| + 2log|x+2|+c
Ex 7.5 Class 12 Maths Question 2.
Solution:
let
⇒ x ≡ A(x+3)+B(x-3)…(i)
put x = 3, -3 in (i)
we get &
Ex 7.5 Class 12 Maths Question 3.
Solution:
Let
⇒ 3x-1 = A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(-2)…..(i)
put x = 1,2,3 in (i)
we get A = 1,B = -5 & C = 4
=log|x-1| – 5log|x-2| + 4log|x+3| + C
Ex 7.5 Class 12 Maths Question 4.
Solution:
let
⇒ x ≡ A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2)…(i)
put x = 1,2,3 in (i)
Ex 7.5 Class 12 Maths Question 5.
Solution:
let
⇒ 2x = A(x+2)+B(x+1)…(i)
put x = -1, -2 in (i)
we get A = -2, B = 4
=-2log|x+1|+4log|x+2|+c
Ex 7.5 Class 12 Maths Question 6.
Solution:
is an improper fraction therefore we
convert it into a proper fraction. Divide 1 – x² by x – 2x² by long division.
Ex 7.5 Class 12 Maths Question 7.
Solution:
let
⇒ x = A(x²+1)+(Bx+C)(x-1)
Put x = 1,0
⇒
Ex 7.5 Class 12 Maths Question 8.
Solution:
⇒ x ≡ A(x-1)(x+2)+B(x+2)+C(x-1)² …(i)
put x = 1, -2
we get
Ex 7.5 Class 12 Maths Question 9.
Solution:
let
⇒ 3x+5 = A(x-1)(x+1)+B(x+1)+C(x-1)
put x = 1,-1,0
we get
Ex 7.5 Class 12 Maths Question 10.
Solution:
Ex 7.5 Class 12 Maths Question 11.
Solution:
let
Ex 7.5 Class 12 Maths Question 12.
Solution:
Ex 7.5 Class 12 Maths Question 13.
Solution:
⇒ 2 = A(1+x²) + (Bx+C)(1 -x) …(i)
Putting x = 1 in (i), we get; A = 1
Also 0 = A – B and 2 = A + C ⇒B = A = 1 & C = 1
Ex 7.5 Class 12 Maths Question 14.
Solution:
=>3x – 1 = A(x + 2) + B …(i)
Comparing coefficients A = -1 and B = -7
Ex 7.5 Class 12 Maths Question 15.
Solution:
⇒ 1 ≡ A(x-1)(x²+1) + B(x+1)(x²+1) + (Cx+D)(x+1)(x-1) ….(i)
Ex 7.5 Class 12 Maths Question 16.
[Hint : multiply numerator and denominator by xn-1 and put xn = t ]
Solution:
Ex 7.5 Class 12 Maths Question 17.
Solution:
put sinx = t
so that cosx dx = dt
Ex 7.5 Class 12 Maths Question 18.
Solution:
put x²=y
Ex 7.5 Class 12 Maths Question 19.
Solution:
put x²=y
so that 2xdx = dy
Ex 7.5 Class 12 Maths Question 20.
Solution:
put x4 = t
so that 4x3 dx = dt
Ex 7.5 Class 12 Maths Question 21.
Solution:
Let ex = t ⇒ ex dx = dt
⇒
Ex 7.5 Class 12 Maths Question 22.
choose the correct answer in each of the following :
(a)
(b)
(c)
(d) log|(x-1)(x-2)|+c
Solution:
(b)
Ex 7.5 Class 12 Maths Question 23.
(a)
(b)
(c)
(d)
Solution:
(a) let
⇒ 1 = A(x²+1)+(Bx+C)(x)
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