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Integral Calculus Previous Year Questions for JEE

20+ syllabus-aligned questions available

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Goodmarks offers 20+ JEE-style PYQs for Integral Calculus with detailed solutions. While official past papers rotate yearly, our bank covers the same concepts, difficulty, and question formats tested in JEE Mathematics.

Previous year questions are the fastest way to understand how Integral Calculus is tested in JEE. Practise 20+ exam-pattern MCQs modelled on JEE Main and Advanced, with full solutions for every question.

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

Free sample questions

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Q1MathsUnit 8: Integral Calculus
Evaluate: ∫12log⁡xdx\int_{1}^{2} \log x d x
Q2MathsUnit 8: Integral Calculus
If In=∫0π/4tan⁡nxdx,I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x, then 1I2+I4,1I3+I5,1I4+I6,…\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
∫(e5log⁡x−e4log⁡xe3log⁡x−e2log⁡x)dx=\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
n→Lt∞[n+1n2+12+n+2n2+22+…+\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. n+nn2+n2]=\left.\frac{\boldsymbol{n}+\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{n}^{2}}\right]=
Q5MathsUnit 8: Integral Calculus
If ∫f(x)log⁡(sin⁡x)dx=log⁡[log⁡sin⁡x]+c\int \frac{\boldsymbol{f}(\boldsymbol{x})}{\log (\sin \boldsymbol{x})} \boldsymbol{d} \boldsymbol{x}=\log [\log \sin \boldsymbol{x}]+\boldsymbol{c} then⁡f(x)=…\operatorname{then} f(x)=\dots
Q6MathsUnit 8: Integral Calculus
Three solid cubes of sides 1cm,6cm1 \mathrm{cm}, 6 \mathrm{cm} and 8cm8 \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=y= −2x+3.-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 : ∫02(x+4)dx\int_{0}^{2}(x+4) d x

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Frequently asked questions

Why practise PYQs for Integral Calculus?

PYQs reveal recurring concepts, common traps, and the difficulty level JEE expects. Solving them builds exam temperament and time management.

Does Goodmarks have actual JEE past papers?

Our bank includes exam-style MCQs aligned with JEE Main Mathematics syllabus for Integral Calculus, covering the same topics as previous year papers.

How should I use PYQs for Integral Calculus?

Solve timed sets, review every explanation, note weak subtopics, then revisit with focused practice on Goodmarks.

Are PYQ solutions step-by-step?

Yes. Every question includes the correct answer and a detailed explanation showing the reasoning.

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