Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Advertisements
उत्तर
The area bounded by the parabola, x2 = y,and the line, y = |x| , can be represented as
The given area is symmetrical about y-axis.
∴ Area OACO = Area ODBO
The point of intersection of parabola, x2 = y, and line, y = x, is A (1, 1).
Area of OACO = Area ΔOAM – Area OMACO
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line `x = a/sqrt2`
The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
Find the area of the region bounded by the following curves, the X-axis, and the given lines:
y = `sqrt(6x + 4), x = 0, x = 2`
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Fill in the blank :
Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.
State whether the following is True or False :
The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy`
Solve the following :
Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
State whether the following statement is True or False:
The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x) "d"x| + |int_"b"^"c" "f"(x) "d"x|`
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5
Find the area of the circle x2 + y2 = 62
The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______
`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.
The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.
The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.
The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
The area bounded by the curve `y = 3/2sqrtx`, the line x = 1 and x-axis is ______ sq. units.
For the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\], which expression for \[y\] is obtained before selecting the first-quadrant branch?
Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?
