Mathematics · JEE

Integral Calculus Mock Test for JEE

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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

\frac{\boldsymbol{x}+\mathbf{2}}{\boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{x}}=

Q4MathsUnit 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=

Q5MathsUnit 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]=

Q6MathsUnit 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

Q7MathsUnit 8: Integral Calculus

\int \sqrt{\frac{\cos x-\cos ^{3} x}{1-\cos ^{3} x}} d x=

Q8MathsUnit 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.

Q9MathsUnit 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.

Q10MathsUnit 8: Integral Calculus

Evaluate the following as the limit of sum :

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

Q11MathsUnit 8: Integral Calculus

It cost Rs 4020 to paint the inner curved surface area of hemisphere of radius 8

m

. If it is painted at rate of Rs. 10 per

m^{2}

. Find inner curved surface.

Q12MathsUnit 8: Integral Calculus

Determine the area of the shaded segment

Q13MathsUnit 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?

Q14MathsUnit 8: Integral Calculus

\int_{-2}^{3} f(x) d x=5

and

\int_{1}^{3}\{2-f(x)\} d x=6

then the value of

\int_{-2}^{1} f(x) d x

is?

Q15MathsUnit 8: Integral Calculus

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

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Frequently asked questions

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For a topic-level test, aim for 20–30 minutes. For a full subject mock, allow 60–90 minutes to mirror JEE timing.

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Aim for 70%+ accuracy initially, then push toward 85%+ as your exam date approaches. Review explanations for every wrong answer.

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