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Home/JEE MAINS/mathematics/application of integrals
Curated PYQ Collection

Top 50 Most Repeated APPLICATION OF INTEGRALS PYQs | JEE MAINS

A curated collection of the most important questions from APPLICATION OF INTEGRALS, fully solved with step-by-step concepts to prepare for JEE MAINS.

Question #1

Practice Question

Concept Applied

Integrate $x = y^2/4$ from $y=-4$ to $4$: $\int_{-4}^{4} \left(4 - \frac{y^2}{4}\right) dy = 32$....

Read Full Step-by-Step Solution →

Question #2

Practice Question

Concept Applied

Area of ellipse $= \pi ab$. Here $a=4$, $b=3$, so area $= 12\pi \approx 37.70\,\text{sq units}$....

Read Full Step-by-Step Solution →

Question #3

Practice Question

Concept Applied

Area $= \int_0^2 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^2 = \frac{8}{3} \approx 2.67$. The integral gives the area under the curve above the x-axi...

Read Full Step-by-Step Solution →

Question #4

Practice Question

A.\frac{128\pi}{5}
B.80\pi
C.\frac{64\pi}{3}
D.\frac{100\pi}{3}

Concept Applied

Using cylindrical shells: \(V = 2\pi\int_{0}^{4} x\sqrt{x}\,dx = 2\pi\int_{0}^{4} x^{3/2}dx = \frac{128\pi}{5}\)....

Read Full Step-by-Step Solution →

Question #5

Practice Question

Concept Applied

Split into intervals [0,2] and [2,3]; integrate piecewise linear function....

Read Full Step-by-Step Solution →

Question #6

Practice Question

Concept Applied

Solve equations to find points of intersection; integrate difference of functions from 0 to 2....

Read Full Step-by-Step Solution →

Question #7

Practice Question

Concept Applied

Using the disk method, $V = \pi\int_{0}^{4}(\sqrt{x})^{2}\,dx = \pi\int_{0}^{4}x\,dx = \pi\left[\frac{x^{2}}{2}\right]_{0}^{4}=8\pi\approx25.13$....

Read Full Step-by-Step Solution →

Question #8

Practice Question

A.$\frac{8}{3}$
B.$\frac{16}{3}$
C.$4$
D.
...

Read Full Step-by-Step Solution →

Question #9

Practice Question

Concept Applied

Integrate $x^2$ from 1 to 3: $\int_1^3 x^2 dx = \left[\frac{x^3}{3}\right]_1^3 = \frac{27}{3} - \frac{1}{3} = 8.67$...

Read Full Step-by-Step Solution →

Question #10

Practice Question

A.A fundamental principle of Mathematics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Application of Integ...

Read Full Step-by-Step Solution →

Question #11

Practice Question

A.Theoretical foundations
B.Practical applications
C.Experimental data
D.Historical context

Concept Applied

Foundational check for Application of Integrals in Class 12. Study the core principles carefully for competitive exams....

Read Full Step-by-Step Solution →

Question #12

Practice Question

Concept Applied

Integrate $x = y^2/4$ from $y=-4$ to $4$: $\int_{-4}^{4} \left(4 - \frac{y^2}{4}\right) dy = 32$....

Read Full Step-by-Step Solution →

Question #13

Practice Question

Concept Applied

Area of ellipse $= \pi ab$. Here $a=4$, $b=3$, so area $= 12\pi \approx 37.70\,\text{sq units}$....

Read Full Step-by-Step Solution →

Question #14

Practice Question

Concept Applied

Area $= \int_0^2 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^2 = \frac{8}{3} \approx 2.67$. The integral gives the area under the curve above the x-axi...

Read Full Step-by-Step Solution →

Question #15

Practice Question

A.\frac{128\pi}{5}
B.80\pi
C.\frac{64\pi}{3}
D.\frac{100\pi}{3}

Concept Applied

Using cylindrical shells: \(V = 2\pi\int_{0}^{4} x\sqrt{x}\,dx = 2\pi\int_{0}^{4} x^{3/2}dx = \frac{128\pi}{5}\)....

Read Full Step-by-Step Solution →

Question #16

Practice Question

Concept Applied

Split into intervals [0,2] and [2,3]; integrate piecewise linear function....

Read Full Step-by-Step Solution →

Question #17

Practice Question

Concept Applied

Solve equations to find points of intersection; integrate difference of functions from 0 to 2....

Read Full Step-by-Step Solution →

Question #18

Practice Question

Concept Applied

Using the disk method, $V = \pi\int_{0}^{4}(\sqrt{x})^{2}\,dx = \pi\int_{0}^{4}x\,dx = \pi\left[\frac{x^{2}}{2}\right]_{0}^{4}=8\pi\approx25.13$....

Read Full Step-by-Step Solution →

Question #19

Practice Question

A.$\frac{8}{3}$
B.$\frac{16}{3}$
C.$4$
D.
...

Read Full Step-by-Step Solution →

Question #20

Practice Question

Concept Applied

Integrate $x^2$ from 1 to 3: $\int_1^3 x^2 dx = \left[\frac{x^3}{3}\right]_1^3 = \frac{27}{3} - \frac{1}{3} = 8.67$...

Read Full Step-by-Step Solution →

Question #21

Practice Question

A.A fundamental principle of Mathematics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Application of Integ...

Read Full Step-by-Step Solution →

Question #22

Practice Question

A.Theoretical foundations
B.Practical applications
C.Experimental data
D.Historical context

Concept Applied

Foundational check for Application of Integrals in Class 12. Study the core principles carefully for competitive exams....

Read Full Step-by-Step Solution →

Question #23

Practice Question

Concept Applied

Integrate $x = y^2/4$ from $y=-4$ to $4$: $\int_{-4}^{4} \left(4 - \frac{y^2}{4}\right) dy = 32$....

Read Full Step-by-Step Solution →

Question #24

Practice Question

Concept Applied

Area of ellipse $= \pi ab$. Here $a=4$, $b=3$, so area $= 12\pi \approx 37.70\,\text{sq units}$....

Read Full Step-by-Step Solution →

Question #25

Practice Question

Concept Applied

Area $= \int_0^2 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^2 = \frac{8}{3} \approx 2.67$. The integral gives the area under the curve above the x-axi...

Read Full Step-by-Step Solution →

Question #26

Practice Question

A.\frac{128\pi}{5}
B.80\pi
C.\frac{64\pi}{3}
D.\frac{100\pi}{3}

Concept Applied

Using cylindrical shells: \(V = 2\pi\int_{0}^{4} x\sqrt{x}\,dx = 2\pi\int_{0}^{4} x^{3/2}dx = \frac{128\pi}{5}\)....

Read Full Step-by-Step Solution →

Question #27

Practice Question

Concept Applied

Split into intervals [0,2] and [2,3]; integrate piecewise linear function....

Read Full Step-by-Step Solution →

Question #28

Practice Question

Concept Applied

Solve equations to find points of intersection; integrate difference of functions from 0 to 2....

Read Full Step-by-Step Solution →

Question #29

Practice Question

Concept Applied

Using the disk method, $V = \pi\int_{0}^{4}(\sqrt{x})^{2}\,dx = \pi\int_{0}^{4}x\,dx = \pi\left[\frac{x^{2}}{2}\right]_{0}^{4}=8\pi\approx25.13$....

Read Full Step-by-Step Solution →

Question #30

Practice Question

A.$\frac{8}{3}$
B.$\frac{16}{3}$
C.$4$
D.
...

Read Full Step-by-Step Solution →

Question #31

Practice Question

Concept Applied

Integrate $x^2$ from 1 to 3: $\int_1^3 x^2 dx = \left[\frac{x^3}{3}\right]_1^3 = \frac{27}{3} - \frac{1}{3} = 8.67$...

Read Full Step-by-Step Solution →

Question #32

Practice Question

A.A fundamental principle of Mathematics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Application of Integ...

Read Full Step-by-Step Solution →

Question #33

Practice Question

A.Theoretical foundations
B.Practical applications
C.Experimental data
D.Historical context

Concept Applied

Foundational check for Application of Integrals in Class 12. Study the core principles carefully for competitive exams....

Read Full Step-by-Step Solution →

Question #34

Practice Question

Concept Applied

Integrate $x = y^2/4$ from $y=-4$ to $4$: $\int_{-4}^{4} \left(4 - \frac{y^2}{4}\right) dy = 32$....

Read Full Step-by-Step Solution →

Question #35

Practice Question

Concept Applied

Area of ellipse $= \pi ab$. Here $a=4$, $b=3$, so area $= 12\pi \approx 37.70\,\text{sq units}$....

Read Full Step-by-Step Solution →

Question #36

Practice Question

Concept Applied

Area $= \int_0^2 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^2 = \frac{8}{3} \approx 2.67$. The integral gives the area under the curve above the x-axi...

Read Full Step-by-Step Solution →

Question #37

Practice Question

A.\frac{128\pi}{5}
B.80\pi
C.\frac{64\pi}{3}
D.\frac{100\pi}{3}

Concept Applied

Using cylindrical shells: \(V = 2\pi\int_{0}^{4} x\sqrt{x}\,dx = 2\pi\int_{0}^{4} x^{3/2}dx = \frac{128\pi}{5}\)....

Read Full Step-by-Step Solution →

Question #38

Practice Question

Concept Applied

Split into intervals [0,2] and [2,3]; integrate piecewise linear function....

Read Full Step-by-Step Solution →

Question #39

Practice Question

Concept Applied

Solve equations to find points of intersection; integrate difference of functions from 0 to 2....

Read Full Step-by-Step Solution →

Question #40

Practice Question

Concept Applied

Using the disk method, $V = \pi\int_{0}^{4}(\sqrt{x})^{2}\,dx = \pi\int_{0}^{4}x\,dx = \pi\left[\frac{x^{2}}{2}\right]_{0}^{4}=8\pi\approx25.13$....

Read Full Step-by-Step Solution →

Question #41

Practice Question

A.$\frac{8}{3}$
B.$\frac{16}{3}$
C.$4$
D.
...

Read Full Step-by-Step Solution →

Question #42

Practice Question

Concept Applied

Integrate $x^2$ from 1 to 3: $\int_1^3 x^2 dx = \left[\frac{x^3}{3}\right]_1^3 = \frac{27}{3} - \frac{1}{3} = 8.67$...

Read Full Step-by-Step Solution →

Question #43

Practice Question

A.A fundamental principle of Mathematics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Application of Integ...

Read Full Step-by-Step Solution →

Question #44

Practice Question

A.Theoretical foundations
B.Practical applications
C.Experimental data
D.Historical context

Concept Applied

Foundational check for Application of Integrals in Class 12. Study the core principles carefully for competitive exams....

Read Full Step-by-Step Solution →

Question #45

Practice Question

Concept Applied

Integrate $x = y^2/4$ from $y=-4$ to $4$: $\int_{-4}^{4} \left(4 - \frac{y^2}{4}\right) dy = 32$....

Read Full Step-by-Step Solution →

Question #46

Practice Question

Concept Applied

Area of ellipse $= \pi ab$. Here $a=4$, $b=3$, so area $= 12\pi \approx 37.70\,\text{sq units}$....

Read Full Step-by-Step Solution →

Question #47

Practice Question

Concept Applied

Area $= \int_0^2 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^2 = \frac{8}{3} \approx 2.67$. The integral gives the area under the curve above the x-axi...

Read Full Step-by-Step Solution →

Question #48

Practice Question

A.\frac{128\pi}{5}
B.80\pi
C.\frac{64\pi}{3}
D.\frac{100\pi}{3}

Concept Applied

Using cylindrical shells: \(V = 2\pi\int_{0}^{4} x\sqrt{x}\,dx = 2\pi\int_{0}^{4} x^{3/2}dx = \frac{128\pi}{5}\)....

Read Full Step-by-Step Solution →

Question #49

Practice Question

Concept Applied

Split into intervals [0,2] and [2,3]; integrate piecewise linear function....

Read Full Step-by-Step Solution →

Question #50

Practice Question

Concept Applied

Solve equations to find points of intersection; integrate difference of functions from 0 to 2....

Read Full Step-by-Step Solution →
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