Advertisements
Advertisements
Question
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Advertisements
Solution
Given equation of the parabola is y2 = 4x
∴ `y = 2sqrt(x)` ...[∵ In first quadrant, y > 0]
And equation of the line is x = 3
∴ Required = Area of the region OQRPO
= 2(Area of the region ORPO)
= `2 int_0^3y.dx`
= `2 int_0^3 2sqrt(x).dx`
= `4 int_0^3 sqrt(x).dx`
= `4 int_0^3 x^(1/2).dx`
= `4[(x^(3/2))/(3/2)]_0^3`
= `4 xx (2)/(3)[(3)^(3/2) - 0]`
= `8/3(3sqrt(3))`
∴ Required area = `8sqrt(3)` sq. units.
APPEARS IN
RELATED QUESTIONS
Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`
Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b = 1`
Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
State whether the following is True or False :
The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy`
If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Choose the correct alternative:
Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______
The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`
The area of the circle x2 + y2 = 16 is ______
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
Find the area of the region bounded by the curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.
The area bounded by the X-axis, the curve y = f(x) and the lines x = 1, x = b is equal to `sqrt("b"^2 + 1) - sqrt(2)` for all b > 1, then f(x) is ______.
The area included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
