Advertisements
Advertisements
प्रश्न
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].
उत्तर
The area bounded by the curve, |x| + |y| = 1 , is represented by the shaded region ADCB as
The curve intersects the axes at points A (0, 1), B (1, 0), C (0, –1), and D (–1, 0).
It can be observed that the given curve is symmetrical about x-axis and y-axis.
∴ Area ADCB = 4 × Area OBAO
APPEARS IN
संबंधित प्रश्न
Find the area of the region lying between the parabolas y2 = 4ax and x2 = 4ay.
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
Using integration finds the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).
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)
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)`
The area bounded by the y-axis, y = cos x and y = sin x when 0 <= x <= `pi/2`
(A) 2 ( 2 −1)
(B) `sqrt2 -1`
(C) `sqrt2 + 1`
D. `sqrt2`
Show that the rectangle of the maximum perimeter which can be inscribed in the circle of radius 10 cm is a square of side `10sqrt2` cm.
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 _______ .
The area between x-axis and curve y = cos x when 0 ≤ x ≤ 2 π is ___________ .
Area enclosed between the curve y2 (2a − x) = x3 and the line x = 2a above x-axis is ___________ .
Area lying between the curves y2 = 4x and y = 2x is
Solve the following :
Find the area of the region lying between the parabolas :
y2 = 4x and x2 = 4y
The area of triangle ΔABC whose vertices are A(1, 1), B(2, 1) and C(3, 3) 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 ellipse `x^2/36 + y^2/64` = 1, using integration
Find the area of the region lying between the parabolas 4y2 = 9x and 3x2 = 16y
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 enclosed by the curve x = 3 cost, y = 2 sint.
Find the area of the region included between the parabola y = `(3x^2)/4` and the line 3x – 2y + 12 = 0.
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.
Draw a rough sketch of the curve y = `sqrt(x - 1)` in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.
Area lying between the curves `y^2 = 4x` and `y = 2x`
Find the area cut off from the parabola 4y = 3x2 by the line 2y = 3x + 12.
