Indefinite Integrals MCQ Quiz - Objective Question with Answer for Indefinite Integrals - Download Free PDF

Last updated on Mar 17, 2025

Latest Indefinite Integrals MCQ Objective Questions

Indefinite Integrals Question 1:

The value of  is

Answer (Detailed Solution Below)

Option 2 :

Indefinite Integrals Question 1 Detailed Solution

Concept:

For Integration with modulus, first we have to find the point where the sign of the value of the function gets change.

Calculation:

Given:

f(x) = 5x - 3 = 0

x = 3/5

∴ from 0 to 3/5 the function is negative and 3/5 to 1 the function is positive.

Indefinite Integrals Question 2:

The value of  is

Answer (Detailed Solution Below)

Option 2 :

Indefinite Integrals Question 2 Detailed Solution

Concept:

For Integration with modulus, first we have to find the point where the sign of the value of the function gets change.

Calculation:

Given:

f(x) = 5x - 3 = 0

x = 3/5

∴ from 0 to 3/5 the function is negative and 3/5 to 1 the function is positive.

Indefinite Integrals Question 3:

 is equal to

  1. e​f(x)
  2. None of these

Answer (Detailed Solution Below)

Option 2 :

Indefinite Integrals Question 3 Detailed Solution

Let,

 

By solving through integration by parts, we get

where C is constant

Indefinite Integrals Question 4:

The value of ∫ log x dx, is

  1. xx + c
  2. x(log x + 1)x + c
  3. x(log x - 1) + c
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : x(log x - 1) + c

Indefinite Integrals Question 4 Detailed Solution


Explanation:

To solve this, we can use

Let   so that 

dv = dx , so that v = x

Now, using integration by parts 

=

So, the correct answer is 

The correct option is option 3.

Indefinite Integrals Question 5:

The value of , is

  1. 2(cos (x/2) - sin (x/2))
  2. 2(sin (x/2) - cos (x/2))
  3. More than one of the above
  4. None of the above

Answer (Detailed Solution Below)

Option 3 : 2(sin (x/2) - cos (x/2))

Indefinite Integrals Question 5 Detailed Solution

Explanation:

2(- cos (x/2) + sin (x/2))

= 2(sin (x/2) - cos (x/2))

(3) is true.

Top Indefinite Integrals MCQ Objective Questions

Let x be a continuous variable defined over the interval (-∞, ∞) and . The integral   is equal to

  1. e-x

Answer (Detailed Solution Below)

Option 2 :

Indefinite Integrals Question 6 Detailed Solution

Download Solution PDF

Substitude e-x = t

-e-x dx = dt

Consider the following definite integral:

The value of the integral is

Answer (Detailed Solution Below)

Option 1 :

Indefinite Integrals Question 7 Detailed Solution

Download Solution PDF

Explanation:

Put sin-1 x = t

The value of , where dA indicate small area in xy-plane, is

  1.  sq. units
  2.  sq. units
  3.  sq. units
  4.  sq. units

Answer (Detailed Solution Below)

Option 2 :  sq. units

Indefinite Integrals Question 8 Detailed Solution

Download Solution PDF

Concept:

Since the inside limit is in terms of x, therefore we have to integrate first the 'y' terms and convert whole expression in terms of x.

Calculation:

Given:

 dx is equal to

  1.  + Constant
  2.  + Constant
  3.  + Constant
  4.  + Constant

Answer (Detailed Solution Below)

Option 3 :  + Constant

Indefinite Integrals Question 9 Detailed Solution

Download Solution PDF

The Given Question is Wrong, Marks are allotted to all.

Explanation-

Given that, 

......

Expanding the options given,

option 1-

option 2-

option 3-

option 4-

So none of the options are matching with the correct answer. 

Answer (Detailed Solution Below)

Option 3 :

Indefinite Integrals Question 10 Detailed Solution

Download Solution PDF

Explanation:

Given Integral 

Let, sin-1 x = t ⇒  as we know the derivative of sin-1 x  =  

Now the equation reduces to 

 ⇒ we know ∫exdx = ex + c 

∴ ∫ etdt = et + c, as t = sin-1 x our equation becomes esin-1x  + c

∴  = 

What is dx equal to ?

  1.  + c
  2.  + c
  3.  + c
  4.  + c

Answer (Detailed Solution Below)

Option 3 :  + c

Indefinite Integrals Question 11 Detailed Solution

Download Solution PDF

Given,

I = 

⇒ I = 

⇒ I =  = I1 - I2 (let)

Computing I1,

I1 = 

Put sin x = t → cos x dx = dt

⇒ I1

⇒ I1 = 

⇒ I1 = 

Similarly, 

I2 = 

Put cos x = t → - sin x dx = dt

⇒ I2 =  

⇒ I2 =  

⇒ I2 =  

Putting these value in I,

⇒ I = I1 - I2 =  - 

⇒ I =  + c

∴ The correct answer is option (3).

 is not true, if n is equal to

  1. 0
  2. 1
  3. 2
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 5 : None of the above

Indefinite Integrals Question 12 Detailed Solution

Download Solution PDF

Explanation:

 is not true for n = -1

because for n = -1

 =  = log |x| + c

(5) is correct

Indefinite Integrals Question 13:

Answer (Detailed Solution Below)

Option 2 :

Indefinite Integrals Question 13 Detailed Solution

Explanation:

Let, t = x2 ⇒ dt = 2xdx ⇒ xdx = dt/2

  

Indefinite Integrals Question 14:

The value of  is

Answer (Detailed Solution Below)

Option 2 :

Indefinite Integrals Question 14 Detailed Solution

Concept:

For Integration with modulus, first we have to find the point where the sign of the value of the function gets change.

Calculation:

Given:

f(x) = 5x - 3 = 0

x = 3/5

∴ from 0 to 3/5 the function is negative and 3/5 to 1 the function is positive.

Indefinite Integrals Question 15:

Let x be a continuous variable defined over the interval (-∞, ∞) and . The integral   is equal to

  1. e-x

Answer (Detailed Solution Below)

Option 2 :

Indefinite Integrals Question 15 Detailed Solution

Substitude e-x = t

-e-x dx = dt

Hot Links: teen patti king lotus teen patti master teen patti teen patti master gold download teen patti master online