Mathematics · JEE

Determining areas of the regions bounded by simple curves in standard forms Concepts for JEE

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Concept explainer

Determining areas of the regions bounded by simple curves in standard forms is a core JEE Main Mathematics subtopic under Integral Calculus. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

Understand the definition and scope of Determining areas of the regions bounded by simple curves in standard forms in the JEE syllabus
Memorise key formulas and standard results linked to Determining areas of the regions bounded by simple curves in standard forms
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Determining areas of the regions bounded by simple curves in standard forms with a one-page formula sheet before attempting mixed tests
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Common trap

Students often rush Determining areas of the regions bounded by simple curves in standard forms questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Integral Calculus in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 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.

Q2MathsUnit 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.

Q3MathsUnit 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.

Q4MathsUnit 8: Integral Calculus

Determine the area of the shaded segment

Q5MathsUnit 8: Integral Calculus

The area of the region bounded by the curve

\boldsymbol{y}=\boldsymbol{x}^{2}+\mathbf{1}

and

\boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{2}

between

x=-1

and

x=2

is:

Q6MathsUnit 8: Integral Calculus

The volume of the global hemisphere is

19404 i n^{3} .

Find its diameter.

Q7MathsUnit 8: Integral Calculus

The area bounded by the

x-

axis, the curve

y=f(x)

and the lines

x=1

and

x=b

is equal to

(\sqrt{b^{2}+1}-\sqrt{2})

for all

\boldsymbol{b}>1,

then

\boldsymbol{f}(\boldsymbol{x})

Q8MathsUnit 8: Integral Calculus

A sphere of radius

3 \mathrm{cm}

is dropped into a cylindrical vessel of radius

4 \mathrm{cm}

. If the sphere is submerged completely, then the height (in cm) to which the water rises, is

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