Advertisements
Advertisements
Question
Find the area bounded by curves {(x, y) : y ≥ x2 and y = |x|}.
Advertisements
Solution
The area bounded by the curves, {(x, y) : y ≥ x2 and y = |x|}., is represented by the shaded region as
It can be observed that the required area is symmetrical about y-axis.
APPEARS IN
RELATED QUESTIONS
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 finds the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).
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)
Area lying between the curve y2 = 4x and y = 2x is
A. 2/3
B. 1/3
C. 1/4
D. 3/4
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].
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`
Using integration, find the area of region bounded by the triangle whose vertices are (–2, 1), (0, 4) and (2, 3).
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 lying between the curves y2 = 4x and y = 2x is
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 the ellipse `x^2/1 + y^2/4` = 1, in first quadrant
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 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.
Find the area of a minor segment of the circle x2 + y2 = a2 cut off by the line x = `"a"/2`
Calcualte the area under the curve y = `2sqrt(x)` included between the lines x = 0 and x = 1
Determine the area under the curve y = `sqrt("a"^2 - x^2)` included between the lines x = 0 and x = a.
Area lying between the curves `y^2 = 4x` and `y = 2x`
Using Integration, find the area of triangle whose vertices are (– 1, 1), (0, 5) and (3, 2).
Find the area enclosed between 3y = x2, X-axis and x = 2 to x = 3.
