Definite Integration JEE Questions PDF with Solution, Practice Now

Definite Integration JEE Questions: Definite Integration is a highly scoring topic in calculus for JEE preparation. It is a part of the JEE Main syllabus and is always given weightage in both JEE Mains and JEE Advanced. Students who have done a good number of problems in definite integration find it scoring in JEE exam. As the name suggests, Definite Integration is the process of finding the area under the curve or the exact value of an integral with limits.: 

There are always multiple questions of calculus every year in the JEE Main exam pattern, and definite integration is not an exception. JEE Main previous year questions indicate that this chapter can come in both direct formula-based and application-based type problems. The chapter can be very difficult in the starting, but with the right amount of practice definite integration can become a high scoring chapter for aspirants.

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Definite Integration JEE Questions Overview

Definite integration in the JEE syllabus has multiple questions based on its types which include direct evaluation, properties application, substitution methods and then some advanced level questions. The concept of definite integration first introduces some basic properties, such as the fundamental theorem of calculus linking differentiation and integration and then properties such as symmetry, periodicity, and substitution methods are taught.

Practice Definite Integration JEE Questions

To score well in JEE, practice is the most important step in definite integration. Students should begin with simple problems based on direct formulas and gradually move towards advanced JEE problems.

1. If In = ∫[0 to π] (sin(2nx)/sin(2x)) dx then the value of I(n/2) (n ∈ I) is

A. nπ/2
B. π
C. π/2
D. 0

2. The number of values of x satisfying the equation ∫[1 to x] (8t²/3 + 28t/3 + 4) dt = 3/(log(x+1) √(x+1)) is

A. 0
B. 1
C. 2
D. 3

3. The value of the definite integral ∫[0 to ∞] (ln x)/(x²+4) dx is

A. (π ln 3)/2
B. (π ln 2)/3
C. (π ln 2)/4
D. (π ln 4)/3

4.

∫ ( e^x ln x + 2/x - 1/x² ) dx =
A. e^x ln x + C1x + C2
B. e^x ln x + 1/x + C1x + C2
C. (ln x)/x + C1x + C2
D. None of these

5. If ∫ (csc²x - 2010)/(cos^2010 x) dx = f(x)/(g(x)^2010) + C, where f(π/4) = 1, then the number of solutions of the equation f(x)/g(x) = {x} in [0, 2π] is

A. 0
B. 1
C. 2
D. 3

6. If ∫ dx/(1+√x)^8 = 1/(3(1+√x)^7) - 1/(7(1+√x)^k1) + C, then

A. k1 = 5
B. k1 = 6
C. k2 = 7
D. k2 = 8

7. If ∫[0 to a] ( e^x + cos x ln(x + √(1+x²)) ) dx > 3/2, then possible value of a can be

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

8. Let ∫ x sin x sec³x dx = 1/2 (x f(x) - g(x)) + C, then

A. f(x) ∈ {-1,1}
B. g(x) = sin x has 6 solutions for x ∈ [-π, 2π]
C. g’(x) = f(x), ∀ x ∈ R
D. f(x) = g(x) has no solution

9. If (sin³θ + sinθ)cosθ e^(inθ) dθ = (A sin³θ + B cos³θ + C sinθ D cosθ + E) e^(inθ) + F, then

A. A = -4
B. B = -12
C. C = -20
D. None of these

10. If f(θ) = lim (r→∞) [2r / (π log(√(30n-2r))(rθ+2r))], then

A. f(θ) = π/2
B. f(θ) = θ/2
C. f(θ) = 0
D. f(θ) is a constant function

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Definite Integration JEE Questions PDF with Solution

Candidates can download a PDF to practice various types of Definite Integration JEE questions, which are prepared based on the JEE syllabus and JEE Main Exam Pattern. The answer key is provided with solutions to help in easy understanding, accuracy and develop robust problem-solving skills.