Advertisements
Advertisements
Question
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.
Solution
Let A be the required area.
A = `int_1^4 y dx`
= `int_1^4 2sqrt(x) dx`
= `2 int_1^4 x^(1/2) dx`
= `2 . 2/3 [x^(3/2)]_1^4`
= `4/3 [4^(3/2) - 1]`
A = `28/3` 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 : 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 : y2 = x, 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 = 2x and y = 2x.
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 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 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 bounded by the ellipse `x^2/a^2 y^2/b^2` = 1 and the line `x/a + y/b` = 1 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 enclosed between the two parabolas y2 = 4x and y = x 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 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 curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).
Solve the following :
Find the area of the region bounded by the straight line 2y = 5x + 7, X-axis and x = 2, x = 5.
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 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 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
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 parabola x2 = 4y and The X-axis and the line x = 1, x = 4
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
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 region bounded by the curves y2 = 4ax and x2 = 4ay
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)
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 line y = 4.
Find the area of the region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.
