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
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
Indefinite Integrals Question 4 Detailed Solution
Explanation:
To solve this, we can use
Let
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
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
Indefinite Integrals Question 6 Detailed Solution
Download Solution PDFSubstitude e-x = t
-e-x dx = dt
Consider the following definite integral:
The value of the integral is
Answer (Detailed Solution Below)
Indefinite Integrals Question 7 Detailed Solution
Download Solution PDFExplanation:
Put sin-1 x = t
The value of
Answer (Detailed Solution Below)
Indefinite Integrals Question 8 Detailed Solution
Download Solution PDFConcept:
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
Answer (Detailed Solution Below)
Indefinite Integrals Question 9 Detailed Solution
Download Solution PDFThe 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)
Indefinite Integrals Question 10 Detailed Solution
Download Solution PDFExplanation:
Given Integral
Let, sin-1 x = t ⇒
Now the equation reduces to
∴ ∫ etdt = et + c, as t = sin-1 x our equation becomes esin-1x + c
∴
What is
Answer (Detailed Solution Below)
Indefinite Integrals Question 11 Detailed Solution
Download Solution PDFGiven,
I =
⇒ I =
⇒ I =
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 =
∴ The correct answer is option (3).
is not true, if n is equal to
Answer (Detailed Solution Below)
Indefinite Integrals Question 12 Detailed Solution
Download Solution PDFExplanation:
because for n = -1
(5) is correct
Indefinite Integrals Question 13:
Answer (Detailed Solution Below)
Indefinite Integrals Question 13 Detailed Solution
Explanation:
Let, t = x2 ⇒ dt = 2xdx ⇒ xdx = dt/2
Indefinite Integrals Question 14:
The value of
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
Indefinite Integrals Question 15 Detailed Solution
Substitude e-x = t
-e-x dx = dt