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Recent questions and answers in Application of Integrals

Questions >> CBSE XII >> Math >> Application of Integrals

Show that the area enclosed by the circle $ x^2+y^2=64a^2$ and the parabola $y^2=12ax$ is $ a^2 \bigg(\frac{16}{\sqrt 3}+\large\frac {64\pi}{\sqrt 3}\bigg)$

answered Apr 1, 2020 by aparme03

1 answer

The area of the region in the first quadrant enclosed by the x-axis,the line y=x and the circle $x^2+y^2=32$ is \begin{array}{1 1}(A)\;16\pi\; sq.units & (B)\;4\pi \;sq.units\\(C)\;32\pi\; sq.units & (D)\;24\pi\;sq.units \end{array}

answered Mar 17, 2020 by kharbans823

2 answers

Find the area of the region enclosed between the circles $ x^2+y^2=1\;and\;\bigg(x-\frac{1}{2}\bigg)^2+y^2=1$

answered Mar 16, 2020 by msq6786

1 answer

Find the area of the segment cut off from the parabola $ y^2=2x$ by the line $ y=4x-1$

answered Dec 22, 2019 by gourishanker2431

1 answer

Find the area bounded by the x-axis part of the curve $ y=1+\Large\frac{8}{x^2}$ and the ordinates x = 2 and x = 4 If the ordinate at x = a divides the area into two equal parts find 'a'

answered Jun 8, 2019 by keerthanapradeeshbabu

1 answer

Find the area included between the parabolas $ y^2=4ax\;and\;x^2=4ay$

answered Dec 25, 2018 by kamaleshtiwari129

2 answers

Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x- axis.$

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.

answered Feb 10, 2014 by rvidyagovindarajan_1

1 answer

Evaluate: $\large \int \limits_{-1}^1 $$x$ $ \left | x \right |$ $ dx$.

asked Feb 10, 2014 by rvidyagovindarajan_1

1 answer

Find the area bounded by curves $x^2 + (y-1)^2 = 1$ and $x^2 + y^2 = 1$.

asked Feb 4, 2014 by rvidyagovindarajan_1

1 answer

Find the area bounded by curves \((x - 1)^2 + y^2 = 1\) and \(x^2 + y^2 = 1.\)

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$

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 $x=2$.

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 \( \frac{\large x}{\large 3}+ \frac{\large y}{\large 2}= 1\)

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

answered Dec 21, 2013 by yamini.v

1 answer

Find the area bounded by the curve $(y = \sin\; x) $ between $ (x = 0) $ and $(x = 2π).$

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

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 $y = 4$.

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$

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).

answered Dec 21, 2013 by yamini.v

1 answer

Find the area between the curves \(y = x\) and \(y = x^2.\)

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 \(x - 3y + 5 = 0\)

answered Dec 21, 2013 by yamini.v

1 answer

Find the area enclosed by the parabola \(4y = 3x^2\) and the line \(2y = 3x + 12.\)

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 \(\Large { \frac{ x}{ a}}+\Large { \frac{y}{ b}} =\normalsize1\)

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 \[ \begin{array}{1} (A)\;2(\pi - 2) \qquad & (B)\;\pi - 2 \qquad &(C)\;2\pi - 1 \qquad & (D)\;2 ( \pi + 2) \end{array} \]

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 $x^2 = 4y$.

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 $(3, 2)$.

answered Dec 21, 2013 by yamini.v

2 answers

Find the area bounded by curves $(x - 1)^2 + y^2 = 1$ and $x^2 + y^2 = 1$.

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 \(x = 3.\)

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 \(x = 4.\)

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

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

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.

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

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.

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 $x^2 + y^2 = 4$.

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 $x = 3$.

answered Dec 20, 2013 by yamini.v

1 answer

Find the area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$.

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 $x =\Large { \frac{a}{\sqrt 2}}$.

answered Dec 20, 2013 by yamini.v

1 answer

Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 4 } + \frac{\Large y^2}{\Large 9} = 1$

answered Dec 20, 2013 by yamini.v

1 answer

Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 16} + \frac{\Large y^2}{\Large 9} = 1$

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 $y^2=6x$.

answered Sep 25, 2013 by sreemathi.v

1 answer

Sketch the graph of y=| x+3 | and evaluate$\Large \int\limits_{-6}^0\normalsize| x+3 |dx$

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 $x=a$.

answered May 8, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by $y=\sqrt x$ and $y=x.$

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 $x+y+2=0.$

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.

answered May 8, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the curve $y^2=2x$ and $x^2+y^2=4x.$

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.

answered May 8, 2013 by sreemathi.v

1 answer

Compute the area bounded by the lines $ x+2y=2,y-x=1\; and\;2x+y=7$

asked Feb 4, 2013 by meena.p

0 answers

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