Mathematics · JEE

Important Questions: Integral Calculus for JEE

20+ syllabus-aligned questions available

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The most important Integral Calculus questions for JEE cover conceptual traps, standard results, and numerical patterns from Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions, Integration by substitution, by parts and by partial fractions, Integration using trigonometric identities, and more. Goodmarks provides 20+ high-yield MCQs with full solutions.

Focus on what matters most. These important Integral Calculus questions cover high-weightage concepts from Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions, Integration by substitution, by parts and by partial fractions, Integration using trigonometric identities, and more — the topics JEE repeats every year.

Subtopics in Integral Calculus

Integral as an anti-derivative
Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions
Integration by substitution, by parts and by partial fractions
Integration using trigonometric identities
Evaluation of simple integrals of standard algebraic/trigonometric forms
The fundamental theorem of calculus, properties of definite integrals
Evaluation of definite integrals
Determining areas of the regions bounded by simple curves in standard forms

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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

\int\left(\frac{e^{5 \log x}-e^{4 \log x}}{e^{3 \log x}-e^{2 \log x}}\right) d x=

Q4MathsUnit 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]=

Q5MathsUnit 8: Integral Calculus

\int \frac{\boldsymbol{f}(\boldsymbol{x})}{\log (\sin \boldsymbol{x})} \boldsymbol{d} \boldsymbol{x}=\log [\log \sin \boldsymbol{x}]+\boldsymbol{c}

\operatorname{then} f(x)=\dots

Q6MathsUnit 8: Integral Calculus

Three solid cubes of sides

1 \mathrm{cm}, 6 \mathrm{cm}

and

8 \mathrm{cm}

respectively are melted to form a new cube. Find the surface area of the cube so formed.

Q7MathsUnit 8: Integral Calculus

Draw the graph of straight line

y=

-2 x+3 .

Use your graph to find the area between the line and co-ordinate axes.

Q8MathsUnit 8: Integral Calculus

Evaluate the following as the limit of sum :

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

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Frequently asked questions

What makes a Integral Calculus 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 Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions, Integration by substitution, by parts and by partial fractions, Integration using trigonometric identities, and more. Prioritise these before moving to edge cases.

How many important questions should I revise?

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

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.