Mathematics · JEE

Important Questions: Evaluation of definite integrals for JEE

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The most important Evaluation of definite integrals questions for JEE cover conceptual traps, standard results, and numerical patterns from Evaluation of definite integrals. Goodmarks provides 6+ high-yield MCQs with full solutions.

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Syllabus context

Part of Integral Calculus in JEE Main Mathematics.

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Q1MathsUnit 8: Integral Calculus

Evaluate:

\int_{1}^{2} \log x d x

Q2MathsUnit 8: Integral Calculus

I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x,

then

\frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}}, \dots

are in

Q3MathsUnit 8: Integral Calculus

\boldsymbol{n} \stackrel{L t}{\rightarrow} \infty\left[\frac{\boldsymbol{n}+\mathbf{1}}{\boldsymbol{n}^{2}+\mathbf{1}^{2}}+\frac{\boldsymbol{n}+\boldsymbol{2}}{\boldsymbol{n}^{2}+\mathbf{2}^{2}}+\ldots+\right.

\left.\frac{\boldsymbol{n}+\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{n}^{2}}\right]=

Q4MathsUnit 8: Integral Calculus

Evaluate the following as the limit of sum :

\int_{0}^{2}(x+4) d x

Q5MathsUnit 8: Integral Calculus

\boldsymbol{I}_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x

then

\frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}}

are in?

Q6MathsUnit 8: Integral Calculus

\int_{100}^{2014} \frac{\sqrt{x}}{\sqrt{2114-x}+\sqrt{x}} d x=

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What makes a Evaluation of definite integrals question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Integral Calculus are high-weightage?

Key areas include Evaluation of definite integrals. Prioritise these before moving to edge cases.

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Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

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