Q. 85.0( 1 Vote )
Evaluate the area bounded by the ellipse above the x-axis.
Given the boundaries of the area to be found are,
• The ellipse,
• y = 0 (x-axis)
From the equation, of the ellipse
• the vertex at (0,0) i.e. the origin,
• the minor axis is the x-axis and the ellipse intersects the x- axis at A(-2,0) and B(2,0).
• the major axis is the y-axis and the ellipse intersects the y- axis at C(3,0) and D(-3,0).
As x and y have even powers, the area of the ellipse will be symmetrical about the x-axis and y-axis.
Here the ellipse, , can be re-written as
• ----- (1)
As given, the boundaries of the re to be found will be
• The ellipse, with vertex at (0,0).
• The x-axis.
Now, the area to be found will be the area under the ellipse which is above the x-axis.
Area of the required region = Area of ABC.
Area of ABC = Area of AOC + Area of BOC
[area of AOC = area of BOC as the ellipse is symmetrical about the y-axis]
Area of ABC = 2 Area of BOC
[Using the formula, ]
[sin-1(1) = 90° and sin-1(0) = 0° ]
The Area of the required region 3π sq. units
Rate this question :
Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y.
Using integration, find the area of the triangle ABC, coordinates of whose vertices are A(4, 1), B(6, 6) and C(8, 4).Mathematics - Board Papers
Sketch the graph of y =|x + 3| and evaluate the area under the curve
y =|x + 3| above x-axis and between
x = – 6 to x = 0
Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 2), (1, 5) and (3, 4).Mathematics - Board Papers
Find the area of the region included between the parabola y2 = x and the line
x + y = 2.