NCERT Solutions for class 12 Maths | Chapter 7 - Integrals

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Questions
1 ∫ |x| dx is equal to
A 1/2 x² + C
B –x2/2 + C
C x|x| + C
D 1/2 x|x| + C

Answer:1/2 x|x| + C
2 Evaluate: Class 12 Maths chapter 7 Integrals
A log|sec x + tan x| – 2 tan(x/2) + C
B log|sec x – tan x| – 2 tan(x/2) + C
C log|sec x + tan x| + 2 tan(x/2) + C
D None of these

Answer:log|sec x + tan x| – 2 tan(x/2) + C
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3 Class 12 Maths chapter 7 Integrals
A a log |tan-1 x| + C
B 1/2(tan-1 x)² + C
C a log (1 + x2) + C
D None of these

Answer:a log |tan-1 x| + C
4 Evaluate: ∫ sec4/3 x cosec8/3 xdx
A 3/5 tan-5/3 x – 3 tan1/3 x + C
B –3/5 tan-5/3 x + 3 tan1/3 + C
C –3/5 tan-05/3 x – 3 tan1/3 + C
D inversely proportional to the surface area

Answer:None of these
5 Evaluate: ∫(2 tan x – 3 cot x)² dx
A -4tan x – cot x – 25x + C
B 4 tan x – 9 cot x – 25x + C
C – 4 tan x + 9 cot x + 25x + C
D 4 tan x + 9 cot x + 25x + C

Answer:4 tan x – 9 cot x – 25x + C
6 Class 12 Maths chapter 7 Integrals dx is equal to
A 1
B 2
C 3
D 4

Answer:4
7 Class 12 Maths chapter 7 Integrals is equal to
A
B
C
D

Answer:
8 ∫tan-1 √xdx is equal to
A (x + 1)tan-1 √x – √x + C
B x tan-1 √x – √x + C
C √x – x tan-1 √x + C
D √x – (x + 1)tan-1 √x + C

Answer:(x + 1)tan-1 √x – √x + C
9 ∫x² sin x³ dx =
A 1/3 cos x³ + c
B –1/3 cos x + c
C −1/3 cos x³ + c
D 1/2 sin² x³ + c

Answer:−1/3 cos x³ + c
10 dθ =
A tan θ – θ + c
B θ + tan θ + c
C θ – tan θ + c
D -θ – cot θ + c

Answer:θ – tan θ + c
11 dx =
A 1 – log 2
B 2
C 1 + log 2
D log 2

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

Answer:π/2
13 dx =
A log 2
B -log 2
C log 2 – 1
D log 4 – 1

Answer:log 2
14 What is the value of dx?
A 3/2
B 1/2
C e
D 1/e

Answer:3/2
15 What is the value of
A 1/2 log(-l)
B log(- 1)
C log 3
D log √3

Answer:log 3
16
A 1
B 2
C π/4
D π2/8

Answer:2
17
A -1
B 0
C 1
D None of these

Answer:0
18 What is the value of
sin³ x cos² xdx?
A 0
B 1
C 1/2
D 2

Answer:0
19 dx is equal to
A 2 (sin x + x cos θ) + C
B 2 (sin x – x cos θ) + C
C 2 (sin x + 2x cos θ) + C
D 2 (sin x – 2x cos θ) + C

Answer:2 (sin x + x cos θ) + C
20 Class 12 Maths chapter 7 Integrals dx =
A log(sin x – cos x)
B x
C log x
D log sin (cos x)

Answer:x

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