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Find the maximum area of a rectangle that can be inscribed in the ellipse . plz. explain in simple way.

^{2}+ y^{2 }<=2ax, y^{2}>=ax, x,y >= 0}Using integration find the area of that part of circle x

^{2}+y^{2}=16, which is exterior to the parabola y^{2}=6x$\mathbf{11}\mathbf{.}\mathbf{}\mathbf{}Aparticlepismovingwithacons\mathrm{tan}tspeedof6m/sinadirection2\hat{i}-\hat{j}-2\hat{k}.Whent=0,Pisatapointwhosepositionvectoris3\hat{i}+4\hat{j}-7\hat{k}.FindthepositionvectoroftheparticlePafter4seconds.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(1\right)18\hat{i}-4\hat{j}-23\hat{k}\left(2\right)19\hat{i}-4\hat{j}-23\hat{k}\left(3\right)19\hat{i}+4\hat{j}-23\hat{k}\left(4\right)19\hat{i}-4\hat{j}+23\hat{k}$

Sketch the region bounded by the curves y=root of 5-x

^{2}and y=|x-1| and find its areathe locus of the foot of perpendicular drawn from the centre of the ellipseX

^{2}+ 3y^{2}=6 on any tangent to it is^{2}=4a^{2}(x-3)and the lines x=3,y=4a. [NCERT Examplar]^{}find the area bounded by y

^{2}= 4x and x^{2}= 4y^{2}=4a^{2}(x-1)and the lines x=1and y=4aFind the area common to the circle x

^{2}+y^{2}=16a^{2}and the parabola y^{2}=6ax.what is the integration of xcotx

find the area bounded by parabolas y

^{2}=4ax and x^{2}=4ay.Draw a rough sketch of the region: y

^{2}= 6ax and x^{2}+y^{2}= 16a^{2}and find the enclosed area using method of integration.The area of the circle

x^{2}+y^{2}= 16 exterior to the parabolay^{2}= 6xisA.B.C.D.find the area of the region included between the parabola y2 = x and the line x + y =2

Find the area of the smaller part of the circle

x^{2}+y^{2}=a^{2}cut off by the linefind the area of the region enclosed between the two circles x^2+y^2=4 and (x-2)^2+y^2=4

The answer: 4 square units.

The link was provided by you relating to this question, but the student could not solve the question. So, please be kind enough to solve the question .

^{2}=ax and x^{2}+y^{2}=4axspecific doubt: i am getting points of intersection of 2 curves as x=0 and x=3a , it is looking wrong

^{2}/16)+(y^{2}/25)=1 using integrationpls answer to this question immdeiately!!!!

using integration find area of triangle with sides x-3y+3=0,x+2y-2=0,3x+y-11=0

prove that the curves y2 = 4x andd x2 = 4y divide the area of the square bounded by x=0 x=4 and y = 4 and y = 0 in three equal parts?

calculate as a limit of sum limit 1 to 2 (3x2-1)

The slope of the line touching both the

parabolas y2 = 4x and x2 = 32y isUsing integration finds the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).

x+2y=2

y-x=1 and

2x+y=7

{(x,y): x

^{2 }+ y^{2 }^{2 }and x^{2}+y^{2}= 2a^{2}touch each otherfind the area of a triangle whose vertices are a(1,3)b(2,5)c(3,4).

1) Find the point P on the parabola y^2 = 4ax such that area parabola, the X-axis and the tangent at P is equal to that of bounded by the parabola, the X-axis and the normal at P.

2) Find the area of the region bounded by C: y = tanx , tangent drawn at C at x = pie/4 and the x- axis.

^{2}=4x and x^{2}=4y(i)the point of intersection of the curves are?? `

(ii)using integration,find the area between the above two curves

Find the area of the region bounded by the curve

y^{2}= 4xand the linex= 3A tangent is drawn to the curve y = f(x) at p(x,y) cuts the x-axis and y -axis at A and B respectively such taht BP= AP =3 :1 , given taht f(1) = 1 then show that curve passes through (2,1/8).

using the method of integration.find the area of the region bounded by the lines 2x+y=4, 3x-2y=6 and x-3y+5=0

y= -|x-1|+1

area bounded by curve y=6x-x2 nd y=x2-2x?

draw a rough sketch of the curve y = sqrt(3x+4) and find the area under the curve, above x-axis and between x=0 and x=4

Find the area of the region in the 1

^{st}quadrant enclosed by the x-axis, the line x=3^{1/2}y and the circle X^{2}+ Y^{2}= 4find the ratio of the areas into which the curves y

^{2}=6x divides the region bounded by x^{2}+y^{2}=16Find the area of that part of circle x

^{2 }+y^{2 }=16 which is exterior to the parabola y^{2 }=6xFind the area of the circle 4

x^{2}+ 4y^{2}= 9 which is interior to the parabolax^{2}= 4yusing integration find the area of the region enclosed between the circles x

^{2 }+ y^{2}= 1 and (x-1)^{2}+ y^{2}=1^{p1}integral_{ -pi}(xsinx)/(e^{x}+1)find the area of the parabola y

^{2}= 4ax bounded by its latus rectumFind the area bounded by the curve y = 2cosx and the x-axis fromx = 0 to x = 2.

integration of x2+x+1/x2-x+1dx

x2=xsquareFind the area enclosed by the parabola 4

y= 3x^{2}and the line 2y= 3x+ 12find the area of the circle x2+y2=a2 by integration.

^{2}/4+y^{2}/9=1using integration find the area bounded

x

^{2}+y^{2}=4 ,(x-2)^{2}+y^{2}=4Prove Sinx/n =6.

the bottom of a rectangle swimming tank is 25 m by 40 m. water is pumped into the tank at the rate of 500 cubic meters per hour.find the rate at which the level of water in the tank is rising.

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)

^{2}x)and find the areabetween the x axis, the curve and the ordinates