Integral Calculus JEE Mains Questions - List Of Most Asked Questions With Solutions

NTA will shortly release the JEE Main Syllabus 2025 at jeemain.nta.ac.in. Last Year, the complete syllabus of JEE Main underwent some major changes. According to the latest syllabus guidelines, the weightage of Maths has dropped to 22.5%. Due to these changes in the syllabus, certain shifts in chapter-wise weightage have been observed. Integral Calculus are among such topics. It’s among the least weightage topics in JEE Main Maths Syllabus 2025. This chapter holds 1.39% weightage in the whole syllabus.

• Integral Calculus is a part of the General Maths section, and every year around 2-3 questions are asked from this chapter. Due to the drop in weightage, you can expect 1-2 questions in JEE Main 2025.
• Integral Calculus in JEE Mains Maths Syllabus 2025 covers all the basic concepts on units and measurements, fundamentals of units, dimensions etc.

Aspirants consider Integral Calculus as one of the Easiest Chapters in Maths for JEE Main 2025. Even though this chapter has the least weightage in the syllabus, to develop a strong foundation in physics, this particular chapter plays a pivotal role. Hence the candidates need to develop a clear understanding of this chapter. The list of most asked questions from this chapter will help the students with their preparation.

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Here are some common integral calculus questions for JEE Main:

• Integration techniques: Forgetting to use the appropriate integration technique
• Constants of integration: Mishandling constants of integration
• Geometric interpretation: Not understanding the geometric interpretation of integrals

Some important topics in integral calculus for JEE Main include:

• Indefinite integrals and basic integration rules
• Definite integrals and properties
• Area under curves and between curves
• Integration by parts and substitution
• Applications in physics, geometry, and engineering
• Differential equations and their basic concepts

To solve integration problems, you can:

• Integrate the function using the power rule
• Plug in both limits of integration, one at a time
• Subtract the results, with the lower limit's result subtracted from the upper limit's result
• The final value is the solution to the integral

Integral Calculus JEE Mains Questions -

List Of Most Asked Questions With Solutions

In the (JEE) Main, the topic of Physics and Measurement often features questions that have appeared multiple times in previous years. Many questions in this section are either repeated or follow similar patterns, with only minor changes, such as different numerical values or slight modifications in wording.Certain questions have been repeated as many as five times.

Here are some of the most frequently asked and repeated questions:

Question: Evaluate ∫(x^2 + 2x + 1)dx

Solution: Solution: (x^3/3) + x^2 + x + C. Explanation: Integrate term by term.

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: The value of ∫0 to π/2 sin^2(x) dx is:

Solution: Solution: π/4. Explanation: Use the identity sin^2(x) = (1 - cos(2x))/2.

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: Find the integral of e^x/(1+e^x).

Solution: Solution: ln(1 + e^x) + C. Explanation: Use substitution u = 1 + e^x.

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: Evaluate ∫sin(x)/(1 + cos^2(x)) dx.

Solution: Solution: ln(1 + cos^2(x)) + C. Explanation: Use substitution u = cos(x).

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: What is the integral of ln(x) with respect to x?

Solution: Solution: xln(x) - x + C. Explanation: Use integration by parts.

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: Find the integral of cos^2(x)dx.

Solution: Solution: (x/2) + (sin(2x)/4) + C. Explanation: Use the double angle identity for cos^2(x).

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: The value of ∫(1/x)dx is:

Solution: Solution: ln|x| + C. Explanation: Standard result of the integral of 1/x.

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: Evaluate ∫e^(3x) dx.

Solution: Solution: (1/3)e^(3x) + C. Explanation: Use the rule for integrating exponential functions.

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: Find the value of ∫sec^2(x)dx.

Solution: Solution: tan(x) + C. Explanation: Standard result for the integral of sec^2(x).

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question: The integral of xln(x)dx is:

Solution: Solution: (x^2/2)ln(x) - x^2/4 + C. Explanation: Use integration by parts.

(This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)