Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
Advertisements
उत्तर
The region bounded by the parabola `y^2` = 16x and
the line x = 4 is the area OACO
The area OACO is symmetrical about x-axis
Area of OACO = 2(Area of OAB)
Area of OACO = `2int_0^4y dx`
=`2int_0^4 4sqrtx dx`
=`8[x^(3/2 )/(3/2)]_0^4`
=`16/3[x^(3/2)]_0^4`
=`16/3(8)=128/3`
Therefore, the required area is `128/3`sq. units.
APPEARS IN
संबंधित प्रश्न
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 bounded by the curve x2 = 4y and the line x = 4y – 2
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Find the area of the region.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y = 5x + 7, x = 2, x = 8
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
Choose the correct alternative:
Area of the region bounded by the curve y = x3, x = 1, x = 4 and the X-axis is ______
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 ______
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
The area of the circle x2 + y2 = 16 is ______
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
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 curve y = 4x3 − 6x2 + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.
The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 is ______.
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
If the area enclosed by y = f(x), X-axis, x = a, x = b and y = g(x), X-axis, x = a, x = b are equal, then f(x) = g(x).
