# MCQs For NCERT Class 12 Mathematics Chapter 7 Integrals

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 7 Integrals with Answers. The following Integrals Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Integrals Class 12 MCQ Questions with Answers

See below Integrals Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

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C

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D

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D

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D

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(a) 0
(b) 1
(c) 2
(d) 3

C

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(a) 1
(b) 2
(c) 3
(d) 4

A

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(a) 2 √2
(b) 2 ( √2 + 1)
(c) 2
(d) 2( √2 -1)

D

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D

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(a) 0
(b) –1
(c) 1
(d) 2

C

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A

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A

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B

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(a) secx – tanx + C
(b) secx + tanx + x +C
(c) secx + tanx + C
(d) secx – tanx + x + C

D

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B

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B

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C

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D

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B

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(a) e + 1
(b) e -1
(c) e
(d) – e

B

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A

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(a) xsin(logx) + C
(b) sin(logx) + C
(c) xcos(logx) + C
(d) cos(logx) + C

B

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D

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(a) 1
(b) 2
(c) –1
(d) 0

D

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C

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(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

A

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C

Question. ∫ tan-1 √x dx 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

A

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D

Case Based MCQs

Integration is the process of finding the antiderivative of a function. In this process, we are provided with the derivative of a function and asked to find out the function (i.e., Primitive) Integra t ion is the inverse process of differentiation.
Let f (x) be a function of x. If there is a function
g(x), such that d d/x (g(x)) = f (x), then g(x) is called an integral of f (x) w.r.t x and is denoted by ∫ f(x)dx = g(x) + c, where c is constant of integration.

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B

Question. ∫(3x + 4)3dx is equal to

A

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B

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(a) 2 tan 2x + c
(b) –2 tan 2x + c
(c) –2 cot 2x + c
(d) 2 cot 2x + c

C

Question. ∫tan2 x dx is equal to
(a) tan x + x + c
(b) – tan x – x + c
(c) – tan x + x + c
(d) tan x – x + c

D

When the inter grand can be expressed as a product of two functions, one of which can be differentiated and the other can be integrated, then we apply integration by parts.
If f(x) = first function (that can be differentiated) and g(x) = second function (that can be integrated), then the preference of this order can be decided by the word “ILATE”, where
I stands for Inverse Trigonometric Function
L stands for Logarithmic Function
A stands for Algebraic Function
T stands for Trigonometric Function
E stands for Exponential Function, then

Question. ∫ x sin3x dx =

B

Question. ∫ log(x +1) dx =
(a) log (x + 1) – x + c
(b) x log(x + 1) – x + c
(c) x log(x + 1) – log (x + 1) + x + c
(d) x log(x + 1) + log (x + 1) – x + c

D

Question. ∫ x2e3x dx =

D

Question. ∫(f(x)g”(x) − f”(x)g(x)) dx =