Indefinite Integration JEE Questions PDF with Solution, Practice Now

Indefinite Integration JEE Questions: In JEE Mains and JEE Advanced, indefinite integration is a part of Calculus. It is an important part of Mathematics in the JEE. Indefinite Integration is one of the major topics of Calculus, which you study in your pre-board exam. You study the theory and are given some simple problems to solve during your school years. The concepts that you study in school are of extreme importance as they have a wide range of applications in various physics and engineering problems. Indefinite Integration carries high weightage in JEE Main and is a frequently asked topic with a total of 6–8% marks for the entire mathematics section.

JEE preparation requires you to solve various types of indefinite integration JEE questions and JEE Advanced calculus questions to help you feel confident when you solve such problems. Students can improve their problem-solving abilities in Mathematics, Physics, and Chemistry through practice questions on JEE Indefinite Integration.

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Indefinite Integration JEE Questions Overview

The topic of indefinite integration in the JEE Main exam paper comprises standard formulas, substitution, integration by parts, special functions, and more. The following important indefinite integration PYQs, which have been asked in the previous JEE exams, would give you an insight into the question pattern. 

 JEE aspirants who are regular in their practice of Indefinite Integration questions not only score well in the Mathematics section but also gain a thorough understanding of the other concepts that are similar to or related to the topic of Indefinite Integration. Some of the similar and related topics are definite integration, differential equations, and areas under the curves. The JEE Main exam paper pattern has both short and long questions for the students to assess their speed and accuracy in solving problems.

Practice Indefinite Integration JEE Questions

Here are some Indefinite Integration JEE Questions for practice:

1. If A = ∫(0 to π/2) (sin x / x²) dx, then ∫(0 to π/2) (cos 2x / x) dx is equal to

A. 1 - A
B. 3/2 - A
C. A - 1
D. 1 + A

2. ∫(√(sec⁵x) / √(sin³x)) dx equals to

A. (tan x)^(3/2) - √tan x + C
B. (2/3) [(tan x)^(3/2) - (1/√tan x)] + C
C. (1/3) (tan x)^(3/2) - √tan x + C
D. √sin x + √cos x + C

3. The value of ∫(0 to 1) lim(n→∞) Σ(k=0 to n) (x^k+2 * 2^k / k!) dx is:

A. e² - 1
B. 2
C. (e² - 1)/2
D. (e² - 1)/4

4. If ∫(0 to 100) f(x) dx = a, then Σ(r=1 to 100) ∫(0 to 1) f((r - 1 + x)) dx =

A. 100a
B. a
C. 0
D. 10a

5. If ∫ (dx / (x⁴(1+x)²)) = a ln |(1+x³)/x³| + b/x³ + c/(1+x³) + d, then (where d is arbitrary constant):

A. a = 1/3, b = 1/3, c = 1/3
B. a = 2/3, b = -1/3, c = 1/3
C. a = 2/3, b = -1/3, c = -1/3
D. a = 2/3, b = -1/3, c = -1/3

6. If ∫(0 to 1) e^(-x²) dx = a, then ∫(0 to 1) x² e^(-x²) dx is equal to

A. (1/2e)(ea - 1)
B. (1/2e)(ea + 1)
C. (1/e)(ea - 1)
D. (1/e)(ea + 1)

7. ∫ (cos 9x + cos 6x) / (2 cos 5x - 1) dx = A sin 4x + B sin x + C, then A + B is equal to:

A. 1/2
B. 3/4
C. 2
D. 5/4

8. Let f(x) = lim(n→∞) (cos x / (1 + (tan⁻¹x)ⁿ)), then ∫(0 to ∞) f(x) dx =

A. tan(sin 1)
B. sin(tan 1)
C. 0
D. sin(tan 1 / 2)

9. ∫ (x² / (x²+1)) e^(cot⁻¹x) dx = F(x) * e^(cot⁻¹x) + C, where C is constant of integration. Then F(x) is equal to:

A. -x
B. √(1 - x)
C. x
D. √(1 + x)

10. lim(n→∞) (1/n³) (√(n²+1) + √(2n²+2²) + … + √(n²+n²)) =

A. (3√2 - 1)/2
B. (2√2 - 1)/2
C. (3√3 - 1)/3
D. (4√2 - 1)/2

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Indefinite Integration JEE Questions PDF with Solution

For better preparation, Physics Wallah brings a Practice PDF of indefinite integration JEE Mains questions with step-by-step answers and solutions, along with important theory points with tips to solve the questions easily and quickly.

Our Indefinite Integration JEE Questions with solutions PDF is prepared according to the JEE exam pattern. So, students can practice questions in a real exam-like environment. Solving this PDF will help the students to revise the topics, improve speed and accuracy and increase confidence to attempt the JEE questions.