Advertisements
Advertisements
प्रश्न
The area of the region bounded by the curve x = y2, y-axis and the line y = 3 and y = 4 is ______.
उत्तर
The area of the region bounded by the curve x = y2, y-axis and the line y = 3 and y = 4 is `37/3` sq.units
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the parabola y2 = 4ax and its latus rectum.
Prove that the curves y2 = 4x and x2 = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.
Sketch the region bounded by the curves `y=sqrt(5-x^2)` and y=|x-1| and find its area using integration.
Area bounded by the curve y = x3, the x-axis and the ordinates x = –2 and x = 1 is ______.
Find the equation of a curve passing through the point (0, 2), given that the sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at that point by 5
Sketch the graph of y = |x + 4|. Using integration, find the area of the region bounded by the curve y = |x + 4| and x = –6 and x = 0.
Sketch the region {(x, y) : 9x2 + 4y2 = 36} and find the area of the region enclosed by it, using integration.
Find the area enclosed by the curve x = 3cost, y = 2sin t.
Find the area of the region in the first quadrant bounded by the parabola y = 4x2 and the lines x = 0, y = 1 and y = 4.
Find the area of the region common to the circle x2 + y2 = 16 and the parabola y2 = 6x.
Find the area of the region bounded by the curve y = \[\sqrt{1 - x^2}\], line y = x and the positive x-axis.
Find the area bounded by the lines y = 4x + 5, y = 5 − x and 4y = x + 5.
If the area bounded by the parabola \[y^2 = 4ax\] and the line y = mx is \[\frac{a^2}{12}\] sq. units, then using integration, find the value of m.
If the area enclosed by the parabolas y2 = 16ax and x2 = 16ay, a > 0 is \[\frac{1024}{3}\] square units, find the value of a.
The area bounded by y = 2 − x2 and x + y = 0 is _________ .
The area bounded by the parabola x = 4 − y2 and y-axis, in square units, is ____________ .
The area bounded by the y-axis, y = cos x and y = sin x when 0 ≤ x ≤ \[\frac{\pi}{2}\] is _________ .
Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is
Find the area of the region bound by the curves y = 6x – x2 and y = x2 – 2x
The area enclosed by the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 is equal to ______.
Find the area of the region bounded by the curve y2 = 4x, x2 = 4y.
Find the area of the region included between y2 = 9x and y = x
Find the area bounded by the curve y = `sqrt(x)`, x = 2y + 3 in the first quadrant and x-axis.
The curve x = t2 + t + 1,y = t2 – t + 1 represents
Find the area of the region bounded by the curve `y^2 - x` and the line `x` = 1, `x` = 4 and the `x`-axis.
Find the area of the region enclosed by the curves y2 = x, x = `1/4`, y = 0 and x = 1, using integration.
The area enclosed by y2 = 8x and y = `sqrt(2x)` that lies outside the triangle formed by y = `sqrt(2x)`, x = 1, y = `2sqrt(2)`, is equal to ______.
For real number a, b (a > b > 0),
let Area `{(x, y): x^2 + y^2 ≤ a^2 and x^2/a^2 + y^2/b^2 ≥ 1}` = 30π
Area `{(x, y): x^2 + y^2 ≥ b^2 and x^2/a^2 + y^2/b^2 ≤ 1}` = 18π.
Then the value of (a – b)2 is equal to ______.
Area (in sq.units) of the region outside `|x|/2 + |y|/3` = 1 and inside the ellipse `x^2/4 + y^2/9` = 1 is ______.
Find the area of the following region using integration ((x, y) : y2 ≤ 2x and y ≥ x – 4).
