Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Let A be the required area.
Given equation of the curve is y = `sqrt(2x + 3)`
∴ A = `int_0^2 y "d"x`
= `int_0^2 sqrt(2x + 3) "d"x`
= `int_0^2 (2x + 3)^(1/2) "d"x`
= `[((2x + 3)^(3/2))/(3/2) xx 1/2]_0^2`
= `1/3[(2x + 3)^(3/2)]_0^2`
= `1/3[(4 + 3)^(5/2) - (0 + 3)^(3/2)]`
= `1/3[(7)^(3/2) - (3)^(3/2)]`
∴ A = `1/3(7sqrt(7) - 3sqrt(3))` sq.units
APPEARS IN
संबंधित प्रश्न
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
`x^2+y^2=4 at (1, sqrt3)`
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Find the area of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).
Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.
Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4
Find the area of the region bounded by the following curve, the X-axis and the given line:
y = 2 – x2, x = –1, x = 1
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______
Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
Find the area of the circle x2 + y2 = 16
The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______
The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 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 ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
The area included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
The area of the region bounded by the curve y = x2, x = 0, x = 3, and the X-axis is ______.
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
