Advertisements
Advertisements
प्रश्न
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
उत्तर
Given equation of the parabola is x2 = 4y
∴ x = `2sqrt(y)` ......[∵ In first quadrant x > 0]
∴ Required area = `int_0^3 2sqrt(y) "d"y`
= `2 int_0^3 sqrt(y) "d"y`
= `3[(y^(3/2))/(3/2)]_0^3`
= `4/3[(3)^(3/2) - 0]`
= `4/3(3sqrt(3))`
= `4sqrt(3)` sq.units
APPEARS IN
संबंधित प्रश्न
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
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 following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4
Find the area of the region bounded by the following curves, the X-axis and the given lines:
y = x2 + 1, x = 0, x = 3
Fill in the blank :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
Fill in the blank :
Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
Choose the correct alternative:
Area of the region bounded by the curve x2 = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 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 region lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 is ______
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
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 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
Area enclosed between the curve y2(4 - x) = x3 and line x = 4 above X-axis is ______.
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
Area bounded by the curves y = `"e"^(x^2)`, the x-axis and the lines x = 1, x = 2 is given to be α square units. If the area bounded by the curve y = `sqrt(ℓ "n"x)`, the x-axis and the lines x = e and x = e4 is expressed as (pe4 – qe – α), (where p and q are positive integers), then (p + q) is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
