Advertisements
Advertisements
Question
Find the area of the region bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4
Solution
The required area consists of two bounded regions A1 and A2 which are equal in areas.
For y2 = x, y = `sqrt(x)`
Required area = A1 + A2 = 2A1
= `2int_0^4 y*dx, "where" y = sqrt(x)`
= `2int_0^4 4 sqrt(x)*dx`
= `8[(x^(3/2))/(3/2)]_0^4`
= `16/3[x^(3/2)]_0^4`
= `16/3[(4)^(3/2) - (0)^(3/2)]`
= `16/3 (8)`
A = `(128)/(3) "sq. units"`.
APPEARS IN
RELATED QUESTIONS
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 parabola: y = 4 – x2 and the X-axis.
Find the area of the region included between y2 = 2x and y = 2x.
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 bounded between the line x = 4 and the parabola y2 = 16x is ______.
Choose the correct option from the given alternatives :
The area under the curve y = `2sqrt(x)`, enclosed between the lines x = 0 and x = 1 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 the parabola y2 = x and the line 2y = x is
Choose the correct option from the given alternatives :
The area bounded by the parabola y = x2 and the line y = x 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 bounded by x2 = 16y, y = 1, y = 4 and x = 0 in the first quadrant, 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 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 bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = `pi/(3)`
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 straight line 2y = 5x + 7, X-axis and x = 2, x = 5.
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 bounded by the parabola y2 = 32x the X-axis and the latus rectum 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 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
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4
Find the area of the region bounded by the curves y2 = 4ax and x2 = 4ay
Find the area of the region bounded by the curve (y − 1)2 = 4(x + 1) and the line y = (x − 1)
The area bounded by the curve y = x3, the X-axis and the Lines x = –2 and x = 1 is ______.
Find the area of the region bounded by the curve y2 = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.
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 of the region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.
