Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4
Advertisements
उत्तर
Given equation of the curve is y2 = 16x
y2 =
∴ y = `+- 4sqrt(x)`
∴ y = `4 sqrt(x)` ......[∵ In first quadrant, y > 0]
Required area = Area of the region OBSAO
= 2 .......(Area of the region OSAO)
= `2int_0^4 y "d"x`
= `2 int_0^4 4sqrt(x) "d"x`
= `8[(x^(3/2))/(3/2)]_0^4`
= `16/3[(4)^(3/2) - 0]`
= `16/3(8)`
= `128/3` sq.units
APPEARS IN
संबंधित प्रश्न
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 : x = 0, x = 5, y = 0, y = 4
Find the area of the region bounded by the following curves, X-axis and the given lines: xy = 2, x = 1, x = 4
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 bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4
Find the area of the region bounded by the parabola y2 = 16x and its latus rectum.
Find the area of the region included between: y2 = 4x, and 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 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 bounded by the curve y = x3, the X-axis and the lines x = – 2 and x = 1 is
The area enclosed between the parabola y2 = 4x and line y = 2x is ______.
The area of the region bounded by y = cos x, Y-axis and the lines x = 0, x = 2π 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 bounded by y = `sqrt(x)` and the x = 2y + 3, X-axis in first quadrant is
Choose the correct option from the given alternatives :
The area bounded by the parabola y = x2 and the line y = x 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
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 bounded by the parabola y2 = x and the line y = x in the first quadrant.
Solve the following:
Find the area of the region lying between the parabolas: 4y2 = 9x and 3x2 = 16y
Solve the following:
Find the area enclosed between the circle x2 + y2 = 1 and the line x + y = 1, lying in the first quadrant.
Solve the following:
Find the area of the region bounded by the curve y = 4x2, Y-axis and the lines y = 1, y = 4.
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
The area bounded by the parabola y2 = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units
The area bounded by the ellipse `x^2/4 + y^2/25` = 1 and the line `x/2 + y/5` = 1 is ______ sq.units
The area enclosed by the line 2x + 3y = 6 along X-axis and the lines x = 0, x = 3 is ______ sq.units
Find the area bounded by the curve y2 = 36x, the line x = 2 in first quadrant
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 curve y = x2, the X−axis and the given lines x = 0, x = 3
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
Find the area of the region bounded by the curve x2 = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 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
Find the area of the sector bounded by the circle x2+ y2 = 16, and the line y = x in the first quadrant
Find the area of the region bounded by the curve (y − 1)2 = 4(x + 1) and the line y = (x − 1)
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 2 and y = 4.
Find the area common to the parabola y2 = x – 3 and the line x = 5.
Find the area of the region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.
