Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the curves x2 = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant
उत्तर
Given equation of the parabola is x2 = 8y
∴ x = `+- 2 sqrt(2y)`
∴ x = `2sqrt(2y)` .....[∵ In first quadrant, x > 0]
∴ Required area = `int_2^4 x "d"y`
= `int_2^4 2sqrt(2y) "d"y`
= `2sqrt(2)[(y^(3/2))/(3/2)]_2^4`
= `(4sqrt(2))/3 [(4)^(3/2) - (2)^(3/2)]`
= `(4sqrt(2))/3 (8 - 2sqrt(2))`
= `(8sqrt(2))/3 (4 - sqrt(2))` sq.units
संबंधित प्रश्न
Find the area of the region bounded by the following curves, X-axis and the given lines: y = 2x, x = 0, x = 5
Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4
Find the area of the region bounded by the following curves, X-axis and the given lines : y = sin x, x = 0, x = `pi/(2)`
Find the area of the region bounded by the following curves, X-axis and the given lines : y2 = x, x = 0, x = 4
Find the area of the region included between: y = x2 and the line y = 4x
Find the area of the region included between: y2 = 4ax and the line y = x
Find the area of the region included between y = x2 + 3 and the line y = x + 3.
Choose the correct option from the given alternatives :
The area bounded by the regional 1 ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by ______.
Choose the correct option from the given alternatives :
The area of the region enclosed by the curve y = `(1)/x`, and the lines x = e, x = e2 is given by
Choose the correct option from the given alternatives :
The area of the region bounded between the line x = 4 and the parabola y2 = 16x is ______.
Choose the correct option from the given alternatives :
The area of the circle x2 + y2 = 25 in first quadrant is
Choose the correct option from the given alternatives :
The area of the region bounded by the ellipse `x^2/a^2 + y^2/b^2` = 1 is
Choose the correct option from the given alternatives :
The area bounded by y = `sqrt(x)` and the x = 2y + 3, X-axis in first quadrant is
The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is ______.
Choose the correct option from the given alternatives :
The area of the region included between the parabolas y2 = 4ax and x2 = 4ay, (a > 0) is given by
Choose the correct option from the given alternatives :
The area of the region included between the line x + y = 1 and the circle x2 + y2 = 1 is
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : 0 ≤ x ≤ 5, 0 ≤ y ≤ 2
Solve the following :
Find the area of the region in first quadrant bounded by the circle x2 + y2 = 4 and the X-axis and the line x = `ysqrt(3)`.
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π
Solve the following :
Find the area of the region lying between the parabolas : 4y2 = 9x and 3x2 = 16y
Solve the following :
Find the area of the region lying between the parabolas : y2 = x and x2 = y.
Solve the following :
Find the area of the region bounded by the curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).
The area of the region bounded by the curve y = sinx, X-axis and the lines x = 0, x = 4π is ______ sq.units
The area of the region bounded by the ellipse x2/64 + y2/100 = 1, is ______ sq.units
Find the area bounded by the curve y = sin x, the lines x = 0 and x = `pi/2`
Find the area of the region bounded by the parabola y2 = 32x and its Latus rectum in first quadrant
Find the area of the region bounded by the curve y2 = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0
Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4
Find the area of the region bounded by the curve y = sin x, the X−axis and the given lines x = − π, x = π
The area bounded by the curve y = x3, the X-axis and the Lines x = –2 and x = 1 is ______.
Find the area common to the parabola y2 = x – 3 and the line x = 5.
Find the area bounded by the lines y = 5x – 10, X-axis and x = 5.
Find the area of the region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.
