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Online Practice: Integral Calculus for JEE

20+ syllabus-aligned questions available

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Goodmarks provides free online JEE practice for Integral Calculus with 20+ MCQs, instant answer checking, and full solutions. Sign up to unlock the complete question bank and topic-wise filters.

Sharpen your mathematics preparation with interactive online practice for Integral Calculus. Goodmarks offers 20+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

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

How do I practice Integral Calculus online for JEE?

Open this page, attempt the free sample MCQs, then sign up on Goodmarks to access the full Integral Calculus question bank with topic filters and detailed explanations.

How many Integral Calculus questions are available?

Goodmarks currently has 20+ JEE-aligned MCQs for Integral Calculus, with more added regularly.

Is this aligned with the JEE Main syllabus?

Yes. All Mathematics questions on Goodmarks are organised by official JEE Main units and subtopics, including 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.

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Every question includes the correct answer and a step-by-step explanation. Free users can practise a random mix; Pro unlocks full subject and topic filters.

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