NCERT Solutions for class 12 Maths | Chapter 7 - Integrals

Questions
1 If Class 12 Maths chapter 7 Integrals dx = log |x – 2| + k log f(x) + c, then
A f(x) = |x² + 2x + 2|
B f(x) = x² + 2x + 2
C k = –1/2
D All of these

Answer:All of these
2 ∫ cos-1(1/x)dx equals
A x sec-1 x + log |x ++C
B x sec-1 x – log |x ++C
C -x sec-1 x – log |x ++C
D None of these

Answer:x sec-1 x – log |x ++C

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3 Class 12 Maths chapter 7 Integrals dx is equal to
A tan x + cos x + c
B tan x + cosec x + c
C tan x + cot x + c
D tan x+ sec x + c

Answer:tan x + cot x + c
4 |x|dx =
A 0
B 2
C 1
D 4

Answer:4
5 Evaluate: ∫(2tan x – 3cot x)2 dx
A -4tan x – 9cot x – 25x + C
B 4tan x – 9cot x – 25x + C
C -4tan x + 9 cot x + 25x + C
D 4tan x + 9cot x + 25x + C

Answer:4tan x – 9cot x – 25x + C
6  If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is
A 7
B -4
C 3
D −1/4

Answer:−1/4
7 ∫cot²x dx equals to
A cot x – x + C
B cot x + x + C
C -cot x + x + C
D -cot x – x + C

Answer:-cot x – x + C
8 ∫1.dx =
A x + k
B 1 + k
C x2/2 + k
D log x + k

Answer:x + k
9 Class 12 Maths chapter 7 Integrals =
A tan x/2 + k
B 1/2 tan x/2 + k
C 2 tan x/2 + k
D tan² x/2 + k

Answer:tan x/2 + k
10 Class 12 Maths chapter 7 Integrals
A 1/3(1+log)³ + c
B 1/2(1+log)² + c
C log (log 1 + x) + 2
D None of these

Answer:1/3(1+log)³ + c
11 dx is equal to
A log |1 + cos x | + c
B log | x + sin x | + c
C x – tan + c
D x. tan x/2 + c

Answer:x. tan x/2 + c
12
A tan x/2 + k
B 1/2 tan x/2 + k
C 2 tan x/2 + k
D tan² x/2 + k

Answer:tan x/2 + k
13
A 1
B π2/64
C π2192
D None of these

Answer:π2192
14 dx is equal to
A
B
C
D

Answer:
15 What is the value of dx?
A 1
B π/2
C 0
D –π/2

Answer:0
16 dx =
A 1 – log 2
B 2
C 1 + log 2
D log 2

Answer:1 – log 2
17 Value of Class 12 Maths chapter 7 Integrals
A sin-1 (x – 1) + c
B sin-1 (1 + x) + c
C sin-1 (1 + x²) + c
D

Answer:sin-1 (x – 1) + c
18 If = a log |1 + x²| + b tan-1 x + 1/5 log |x + 2| + C, then
A a = −1/10, b = −2/5
B a = 1/10, b = −2/5
C a = −1/10, b = 2/5
D a = 1/10, b = 2/5

Answer:a = −1/10, b = −2/5
19 Evaluate: dx
A -sin-1 (x−4/5) + C
B sin-1 (x+4/5) + C
C sin-1 (x−4/5) + C
D None of these

Answer:sin-1 (x−4/5) + C
20 Class 12 Maths chapter 7 Integrals
A
B
C
D

Answer:

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