Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the parabola: y = 4 – x2 and the X-axis.
उत्तर
The equation of the parabola is y = 4 – x2
∴ x2 = 4 – y, i.e. (x – 0)2 = – (y – 4)
It has vertex at P(0, 4).
For points of intersection of the parabola with X-axis, we put y = 0 in its equation.
∴ 0 = 4 – x2
∴ x2 = 4
∴ x = ± 2.
∴ The parabola intersect the X-axis at A(– 2, 0) and B(2, 0)
Required area = Area of the region APBOA
= 2[Area of the region OPBO]
= `2int_0^2 y dx, "where" y = 4 - x^2`
= `2int_0^2 (4 - x^2)dx`
= `8int_0^2 1dx - 2 int_0^2x^2 dx`
= `8[x]_0^2 - 2[x^3/3]_0^2`
= `8(2 - 0) - 2/3(8 - 0)`
= `16 - 16/3`
= `32/3` sq units.
APPEARS IN
संबंधित प्रश्न
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 following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4
Find the area of the region included between: y = x2 and the line y = 4x
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 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 ______.
The area of the region bounded by y = cos x, Y-axis and the lines x = 0, x = 2π 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 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 parabola y = x2 and the line y = x 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 line x + y = 1 and the circle x2 + y2 = 1 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 lying between the parabolas : 4y2 = 9x and 3x2 = 16y
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
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 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
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 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 region bounded by the curve (y − 1)2 = 4(x + 1) and the line y = (x − 1)
Find the area common to the parabola y2 = x – 3 and the line x = 5.
Find the area bounded by the lines y = 5x – 10, X-axis and x = 5.
