Definite Integration - JEE Main Previous Year Question with Solutions
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Frequently Asked Questions
Find answers to common questions.
Is definite integration hard for JEE Main compared to JEE Advanced?
Definite integration in JEE Main is significantly more formula-driven and property-based. JEE Advanced questions demand deeper insight — such as integral inequalities and parameter-based problems. For JEE Main, mastering the seven standard properties and GIF splitting technique is sufficient for full marks on this topic.
Which property of definite integrals is most important for JEE Main?
King's Property — $\int_a^b f(x)\,dx = \int_a^b f(a+b-x)\,dx$ — is the single most important property for JEE Main. It appears directly or indirectly in roughly 50–60% of definite integration questions asked in the exam, often allowing you to solve the problem in one or two steps.
How many questions on definite integration appear in JEE Main each year?
JEE Main typically includes 2–3 questions on definite integration per session, contributing 8–12 marks. Based on analysis of NTA papers from 2009 to 2023, at least one question every year is directly solvable using King's Property without evaluating the integral in full.
Can I score full marks in the integration section of JEE Main without studying indefinite integration?
No. Definite integration relies on evaluating antiderivatives, so indefinite integration techniques — substitution, integration by parts, partial fractions — are prerequisites. However, for many JEE Main questions, smart property application means you never need to find the antiderivative at all.
How do I solve definite integrals involving the greatest integer function in JEE Main?
Identify all points in $[a, b]$ where the expression inside $[\,.\,]$ takes an integer value. Split the integral at each of those points. Within each sub-interval, $[f(x)]$ is constant, so the integral reduces to a simple polynomial or trigonometric integral. Always list breakpoints before computing — this prevents sign errors.
What is the King's Rule in definite integration?
King's Rule states that $\int_a^b f(x)\,dx = \int_a^b f(a+b-x)\,dx$. In practice, you substitute $x \to a+b-x$ in the integrand. When the original integral and its transformed version are added, the integrand simplifies to a constant, making evaluation straightforward. It is especially powerful for trigonometric and logarithmic integrals.
Where can I find more JEE Main Maths previous year questions with solutions?
eSaral provides chapter-wise JEE Main PYQs with full solutions across all Mathematics topics, taught by IIT Bombay faculty. You can also access the aligned theory through NCERT Solutions for Class 12 Maths and NCERT Solutions for Class 11 Maths on eSaral.