Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the curves x = at2 and y = 2at between the ordinate corresponding to t = 1 and t = 2.
उत्तर
Given that x = at2 ......(i)
y = 2at ......(ii)
t = `y/(2"a")`
Putting the value of t in (i)
Wwe get y2 = 4ax
Putting t = 1 and t = 2 in (i)
We get x = a, and x = 4a
Required area = 2 area of ABCD
= `2 int_"a"^(4"a") y"d"x`
= `2 xx 2 int_"a"^(4"a") sqrt("a"x) "d"x`
= `8sqrt("a") |(x)^(3/2)/3|_"a"^(4"a")`
= `56/3 "a"^2` sq.units
APPEARS IN
संबंधित प्रश्न
Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y
Find the area bounded by curves (x – 1)2 + y2 = 1 and x2 + y 2 = 1
Find the area of the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 3
Using integration find the area of the triangular region whose sides have the equations y = 2x +1, y = 3x + 1 and x = 4.
Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is
A. 2 (π – 2)
B. π – 2
C. 2π – 1
D. 2 (π + 2)
Using the method of integration find the area bounded by the curve |x| + |y| = 1 .
[Hint: The required region is bounded by lines x + y = 1, x– y = 1, – x + y = 1 and
– x – y = 1].
Find the area bounded by curves {(x, y) : y ≥ x2 and y = |x|}.
Choose the correct answer The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is
A. `4/3 (4pi - sqrt3)`
B. `4/3 (4pi + sqrt3)`
C. `4/3 (8pi - sqrt3)`
D.`4/3 (4pi + sqrt3)`
Using integration, find the area of region bounded by the triangle whose vertices are (–2, 1), (0, 4) and (2, 3).
Find the area included between the parabolas y2 = 4ax and x2 = 4by.
The area enclosed between the curves y = loge (x + e), x = loge \[\left( \frac{1}{y} \right)\] and the x-axis is _______ .
Area lying between the curves y2 = 4x and y = 2x is
The area of the region included between the parabolas y2 = 16x and x2 = 16y, is given by ______ sq.units
The area enclosed between the two parabolas y2 = 20x and y = 2x is ______ sq.units
Find the area enclosed between y = cos x and X-axis between the lines x = `pi/2` and x ≤ `(3pi)/2`
Find the area of sector bounded by the circle x2 + y2 = 25, in the first quadrant−
Find the area enclosed between the X-axis and the curve y = sin x for values of x between 0 to 2π
Find the area of the region included between y = x2 + 5 and the line y = x + 7
Find the area enclosed between the circle x2 + y2 = 9, along X-axis and the line x = y, lying in the first quadrant
Find the area of a minor segment of the circle x2 + y2 = a2 cut off by the line x = `"a"/2`
Determine the area under the curve y = `sqrt("a"^2 - x^2)` included between the lines x = 0 and x = a.
The value of a for which the area between the curves y2 = 4ax and x2 = 4ay is 1 sq.unit, is ______.
Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve 4x3 – 3xy2 + 6x2 – 5xy – 8y2 + 9x + 14 = 0 at the point (–2, 3) be A. Then 8A is equal to ______.
Find the area enclosed between 3y = x2, X-axis and x = 2 to x = 3.
Find the area cut off from the parabola 4y = 3x2 by the line 2y = 3x + 12.
