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Recent questions and answers in Application of Integrals
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CBSE XII
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Application of Integrals
Find the area included between the parabolas $ y^2=4ax\;and\;x^2=4ay$
cbse
class12
additionalproblem
kvquestionbank2012
ch8
q3
p31
math
answered
May 24
by
sai.manohar044
1
answer
Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x- axis.$
cbse
class12
maths
ch8
sec-e
answered
Dec 8, 2016
by
priyanka.c
1
answer
Sketch the region and find the area bounded between $y=\sqrt {5-x^2}$ and $y=|x-1|$ using integration.
cl3079
cbse
class12
ch8
q8
p176
short-answer
exemplar
sec-c
difficult
math
answered
Feb 10, 2014
by
rvidyagovindarajan_1
1
answer
Evaluate: $\large \int \limits_{-1}^1 $$x$ $ \left | x \right |$ $ dx$.
cl1124
cbse
class12
bookproblem
ch8
misc
q17
p376
sec-a
medium
math
answered
Feb 10, 2014
by
rvidyagovindarajan_1
1
answer
Find the area bounded by curves \(x^2 + (y-1)^2 = 1\) and \(x^2 + y^2 = 1.\)
class12
cbse
additionalproblem
ch8
sec-c
medium
math
asked
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
Find the area bounded by curves \((x - 1)^2 + y^2 = 1\) and \(x^2 + y^2 = 1.\)
cbse
class12
bookproblem
ch8
sec2
q2
p371
sec-b
medium
math
answered
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
Find the area under the given curves and given lines: $ (ii)\:y = x^4, x = 1, x = 5 \: and\: x - axis$
cbse
class12
bookproblem
ch8
misc
q1
q1-2
p375
sec-a
math
answered
Dec 23, 2013
by
yamini.v
1
answer
Find the area enclosed by the curve $y^2+1=x,x\leq 2$ and the line $x=2$.
class12
cbse
additionalproblem
ch8
sec-b
easy
math
jeemain
integral-calculus
aims-12-math
answered
Dec 22, 2013
by
balaji.thirumalai
1
answer
Find the area of the smaller region bounded by the ellipse \( \frac{\large x^2}{\large 9} + \frac{\large y^2}{\large 4} =1\) and the line \( \frac{\large x}{\large 3}+ \frac{\large y}{\large 2}= 1\)
cbse
class12
bookproblem
ch8
misc
q8
p375
sec-b
easy
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Choose the correct answer in the the area bounded by the \(y\) - axis, \(y = \cos\: x\) and \(y = \sin\: x\) when \(0 \leq x \leq \frac{\large \pi}{2}\) is
cbse
class12
bookproblem
ch8
misc
q19
p376
sec-c
difficult
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area bounded by the curve \(y = \sin\: x\) between \(x = 0\) and \(x = 2Ï€\).
cbse
class12
bookproblem
ch8
misc
q5
p375
sec-a
easy
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Choose the correct answer in the area bounded by the curve\( y = x^3\), the \(x\) - axis and the ordinates \(x = -2\) and \(x = 1\) is
cbse
class12
bookproblem
ch8
misc
q16
p376
sec-a
easy
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area of the region lying in the first quadrant and bounded by \(y = 4x^2, x = 0, y = 1\) and \(y = 4.\)
cbse
class12
bookproblem
ch8
misc
q3
p375
sec-a
medium
math
aims-12-math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area under the given curves and given lines: $ (i) \: y = x^2, x = 1, x = 2 \: and\: x - axis$
cbse
class12
bookproblem
ch8
misc
q1
q1-1
p375
sec-a
easy
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).
cbse
class12
bookproblem
ch8
misc
q13
p376
sec-b
medium
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area between the curves \(y = x\) and \(y = x^2.\)
cbse
class12
bookproblem
ch8
misc
q2
p375
sec-b
easy
math
answered
Dec 21, 2013
by
yamini.v
2
answers
Using the method of integration find the area of the region bounded by lines: \(2x + y = 4, 3x - 2y = 6\) and \(x - 3y + 5 = 0\)
cbse
class12
bookproblem
ch8
misc
q14
p376
sec-c
medium
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area enclosed by the parabola \(4y = 3x^2\) and the line \(2y = 3x + 12.\)
cbse
class12
bookproblem
ch8
misc
q7
p375
sec-c
easy
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area of the smaller region bounded by the ellipse \(\Large { \frac{ x^2}{ a^2}}+\Large { \frac{ y^2}{ b^2}} =\normalsize 1\) and the line \(\Large { \frac{ x}{ a}}+\Large { \frac{y}{ b}} =\normalsize1\)
cbse
class12
bookproblem
ch8
misc
q9
p375
sec-b
medium
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Choose the correct answer in the smaller area enclosed by the circle \(x^2 + y^2 = 4\) and the line \(x + y = 2\) is \[ \begin{array}{1} (A)\;2(\pi - 2) \qquad & (B)\;\pi - 2 \qquad &(C)\;2\pi - 1 \qquad & (D)\;2 ( \pi + 2) \end{array} \]
cbse
class12
bookproblem
ch8
sec2
q6
p372
sec-b
medium
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area of the circle \(4x^2 + 4y^2 = 9\) which is interior to the parabola \(x^2 = 4y.\)
cbse
class12
bookproblem
ch8
sec2
q1
p371
sec-c
medium
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Using integration find the area of region bounded by the triangle whose vertices are $(-1, 0), (1, 3) $ and $(3, 2)$.
cbse
class12
bookproblem
ch8
sec2
q4
p371
sec-c
difficult
math
answered
Dec 21, 2013
by
yamini.v
2
answers
Find the area bounded by curves \((x - 1)^2 + y^2 = 1\) and \(x^2 + y^2 = 1.\)
cbse
class12
bookproblem
ch8
sec2
q2
p371
sec-c
medium
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Find the area of the region bounded by the curves \(y = x^2 + 2, y = x, \: x = 0\) and \(x = 3.\)
cbse
class12
bookproblem
ch8
sec2
q3
p371
sec-b
easy
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Using integration find the area of the triangular region whose sides have the equations \(y = 2x + 1, y = 3x + 1\) and \(x = 4.\)
cbse
class12
bookproblem
ch8
sec2
q5
p371
sec-b
easy
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Choose the correct answer in the area lying between the curves \(y^2 = 4x\) and \(y = 2x\) is
cbse
class12
bookproblem
ch8
sec2
q7
p372
sec-b
medium
math
answered
Dec 21, 2013
by
yamini.v
1
answer
Choose the correct answer in the area of the region bounded by the curve \(y^2 = 4x\), \(y\) - axis and the line \(y = 3\) is
cbse
class12
bookproblem
ch8
sec1
q13
p366
sec-a
easy
math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the region bounded by the curve \(y^2 = x\) and the lines \(x = 1, x = 4\) and the \(x\) - axis.
cbse
class12
bookproblem
ch8
sec1
q1
p365
sec-b
easy
math
aims-12-math
answered
Dec 20, 2013
by
yamini.v
1
answer
Choose the correct answer in area lying in the first quadrant and bounded by the circle \(x^2 + y^2 = 4\) and the lines \(x = 0\) and \(x = 2\) is
cbse
class12
bookproblem
ch8
sec1
q12
p366
sec-a
easy
math
aims-12-math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the region bounded by \(y^2 = 9x,\; x = 2,\; x = 4\) and the \(x\) - axis in the first quadrant.
cbse
class12
bookproblem
ch8
sec1
q2
p365
sec-a
easy
math
aims-12-math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the region in the first quadrant enclosed by \(x\) - axis, line \(x = \sqrt {3}\: y\) and the circle \(x^2 + y^2 = 4.\)
cbse
class12
bookproblem
ch8
sec1
q6
p366
sec-c
medium
math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3.\)
cbse
class12
bookproblem
ch8
sec1
q11
p366
sec-b
easy
math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area bounded by the curve \(x^2 = 4y\) and the line \(x = 4y - 2.\)
cbse
class12
bookproblem
ch8
sec1
q10
p366
sec-c
medium
math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the smaller part of the circle \(x^2 + y^2 = a^2\) cut off by the line \( x =\Large { \frac{a}{\sqrt 2}}.\)
cbse
class12
bookproblem
ch8
sec1
q7
p366
sec-b
easy
math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the region bounded by the ellipse\( \frac{\Large x^2}{\Large 4 } + \frac{\Large y^2}{\Large 9} = 1\)
cbse
class12
bookproblem
ch8
sec1
q5
p366
sec-a
easy
math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the region bounded by the ellipse \( \frac{\Large x^2}{\Large 16} + \frac{\Large y^2}{\Large 9} = 1\)
cbse
class12
bookproblem
ch8
sec1
q4
p366
sec-a
medium
math
answered
Dec 20, 2013
by
yamini.v
1
answer
Find the area of the part of the circle \( x^2+y^2=16\) which is exterior to the parabola \( y^2=6x\).
cbse
class12
modelpaper
2012
sec-c
q25
medium
ch8
math
answered
Sep 25, 2013
by
sreemathi.v
1
answer
Sketch the graph of y=| x+3 | and evaluate$\Large \int\limits_{-6}^0\normalsize| x+3 |dx$
cbse
class12
bookproblem
ch8
misc
q4
p375
modelpaper
2012
q26
math
sec-c
answered
Sep 10, 2013
by
sreemathi.v
1
answer
Determine the area under the curve $y=\sqrt{a^2-x^2}$ included between the lines $x=0$ and $x=a$.
cbse
class12
ch8
q12
p177
short-answer
exemplar
sec-c
medium
math
answered
May 8, 2013
by
sreemathi.v
1
answer
Find the area of the region bounded by $y=\sqrt x$ and $y=x.$
cbse
class12
ch8
q13
p177
short-answer
exemplar
sec-c
medium
math
answered
May 8, 2013
by
sreemathi.v
1
answer
Find the area of the enclosed by the curve $y=-x^2$ and the straight line $x+y+2=0.$
cbse
class12
ch8
q14
p177
short-answer
exemplar
sec-c
difficult
math
answered
May 8, 2013
by
sreemathi.v
1
answer
Find the area bounded by the curve $y=\sqrt x,x=2y+3$ in the first quadrant and $x$-axis.
cbse
class12
ch8
q15
p177
short-answer
exemplar
sec-c
difficult
math
answered
May 8, 2013
by
sreemathi.v
1
answer
Find the area of the region bounded by the curve $y^2=2x$ and $x^2+y^2=4x.$
cbse
class12
ch8
q16
p177
exemplar
sec-c
difficult
math
answered
May 8, 2013
by
sreemathi.v
1
answer
Find the area of region bounded by the triangle whose vertices are $(-1,1),(0,5)$ and $(3,2)$ using integration.
cbse
class12
ch8
q18
p177
exemplar
sec-c
difficult
math
answered
May 8, 2013
by
sreemathi.v
1
answer
The area of the region bounded by the curve $x=2y+3$ and the y-lines $y=1$ and $y=-1$ is \[(A)\;4 sq.units\quad(B)\;\frac{3}{2} sq. units\quad(C)\;6 sq.units\quad(D)8 sq.units\]
cbse
class12
ch8
q34
p178
objective
exemplar
sec-b
easy
math
answered
May 7, 2013
by
sreemathi.v
1
answer
The area of the region bounded by the curve $y=x+1$ and the lines $x=2$ and $x=3$ is \[(A)\frac{7}{2} sq.units\quad(B)\;\frac{9}{2}sq. units\quad(C)\frac{11} {2}sq.units\quad(D)\frac{13}{2} sq.units\]
cbse
class12
ch8
q33
p178
objective
exemplar
sec-b
easy
math
answered
May 7, 2013
by
sreemathi.v
1
answer
The area of the region bounded by the circle $x^2+y^2=1$ is \[(A)\;2\pi sq.units\quad(B)\;\pi sq. units\quad(C)\;3\pi sq.units\quad(D)4\pi sq.units\]
cbse
class12
ch8
q32
p178
objective
exemplar
sec-b
easy
math
answered
May 7, 2013
by
sreemathi.v
1
answer
The area of the region bounded by the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ is \begin{array}{1 1}(A)\;2 \pi sq.units & (B)\;20{\pi}^2 sq.units\\(C)\;16{\pi}^2 sq.units & (D)\;25\pi sq.units \end{array}
cbse
class12
ch8
q31
p178
objective
exemplar
sec-b
medium
math
answered
May 7, 2013
by
sreemathi.v
1
answer
The area of the region bounded by parabola $y^2=x$ and the straight line $2y=x$ is \begin{array}{1 1}(A)\;\frac{4}{3} sq.units & (B)\;1 sq.units\\(C)\;\frac{2}{3} sq.units & (D)\;\frac{1}{3}sq.units \end{array}
cbse
class12
ch8
q29
p178
objective
exemplar
sec-b
medium
math
answered
May 7, 2013
by
sreemathi.v
1
answer
The area of the region bounded by the curve $y=sin x$ between the ordinates $x=0$ and $x=\large\frac{\pi}{2}$ and the x-axis is
cbse
class12
ch8
q30
p178
objective
exemplar
sec-b
easy
math
answered
May 7, 2013
by
sreemathi.v
1
answer
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