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Integral Calculus Previous Year Questions for JEE

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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
x+2x3−x=\frac{\boldsymbol{x}+\mathbf{2}}{\boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{x}}=
Q4MathsUnit 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=
Q5MathsUnit 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]=
Q6MathsUnit 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
Q7MathsUnit 8: Integral Calculus
∫cos⁡x−cos⁡3x1−cos⁡3xdx=\int \sqrt{\frac{\cos x-\cos ^{3} x}{1-\cos ^{3} x}} d x=
Q8MathsUnit 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.

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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.

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

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

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