Advertisements
Advertisements
Question
Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4
Solution
Required area = `int_0^4 x*dy, "where" x = 2y`
= `int_0^4 2y*dy`
= `[(2y^2)/2]_0^4`
= 16 – 0
= 16 sq units.
RELATED QUESTIONS
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: xy = 2, x = 1, 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 bounded by the parabola: y = 4 – x2 and the X-axis.
Find the area of the region included between: y2 = 4x, and y = x
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 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 ______.
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 bounded by the parabola y2 = 8x, the X-axis and the latus rectum 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 the parabola y2 = x and the line 2y = x is
Choose the correct option from the given alternatives :
The area enclosed between the curve y = cos 3x, 0 ≤ x ≤ `pi/(6)` and the X-axis is
Choose the correct option from the given alternatives :
The area enclosed between the two parabolas y2 = 4x and 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 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 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 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 curve y2 = x2, and the line x = 8 is ______
Find the area bounded by the curve y2 = 36x, the line x = 2 in first quadrant
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 parabola x2 = 4y and The X-axis and the line x = 1, x = 4
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 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
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 y = x2, and the lines x = 1, x = 2, and y = 0.
