Q1MathsUnit 8: Integral Calculus
Three solid cubes of sides and respectively are melted to form a new cube. Find the surface area
of the cube so formed.
Mathematics · JEE
Determining areas of the regions bounded by simple curves in standard forms Short Tricks for JEE
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Quick answer
Short tricks for Determining areas of the regions bounded by simple curves in standard forms work only with strong fundamentals. Apply the tips below in timed sets and review every explanation.
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Short tricks for speed
Determining areas of the regions bounded by simple curves in standard forms focus drill
Solve 15 mixed MCQs for Determining areas of the regions bounded by simple curves in standard forms, review every explanation, and note formulas you hesitated on.
Calculus substitution scan
Spot standard forms (sin²x, 1/(a²+x²), e^ax) before integrating — JEE rewards pattern recognition.
Graph sketch shortcut
For coordinate geometry, mark intercepts and asymptotes first; many MCQs need only qualitative graph features.
Syllabus context
Part of Integral Calculus in JEE Main Mathematics.
- 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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Q2MathsUnit 8: Integral Calculus
Draw the graph of straight line
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 . If it is painted at rate of Rs.
10 per . 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 and
between and is:
Q6MathsUnit 8: Integral Calculus
The volume of the global hemisphere is Find its diameter.
Q7MathsUnit 8: Integral Calculus
The area bounded by the axis, the
curve and the lines and
is equal to for all
then is
Q8MathsUnit 8: Integral Calculus
A sphere of radius is dropped into a cylindrical vessel of radius . If the sphere is submerged completely, then the height (in cm) to which the water
rises, is
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Popular questions in Determining areas of the regions bounded by simple curves in standard forms
- The area bounded by the \( x- \) axis, the curve \( y=f(x) \) and the lines \( x=1 \) and \( x=b \) is equal to \( (\sqr…
- The area of the region bounded by the curve \( \boldsymbol{y}=\boldsymbol{x}^{2}+\mathbf{1} \) and \( \boldsymbol{y}=\ma…
- Three solid cubes of sides \( 1 \mathrm{cm}, 6 \mathrm{cm} \) and \( 8 \mathrm{cm} \) respectively are melted to form a …
- Draw the graph of straight line \( y= \) \( -2 x+3 . \) Use your graph to find the area between the line and co-ordinate…
- 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…
- The area of the region bounded by the curve \( \boldsymbol{y}=\boldsymbol{x}^{2}+\mathbf{1} \) and \( \boldsymbol{y}=\ma…
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