Mathematics · JEE

Important Questions: Determining areas of the regions bounded by simple curves in standard forms for JEE

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Part of Integral Calculus in JEE Main Mathematics.

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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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