Advertisements
Advertisements
प्रश्न
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
Advertisements
उत्तर
Given equation of the parabola is x2 = 36y
∴ x = `6sqrt(y)` .....[∵ In first quadrant x > 0]
∴ Required area = area of the region ABCDEFA
= 2(area of the region BCDEB)
= `2 int_1^4 x "d"y`
= `2 int_1^4 6sqrt(y) "d"y`
= `12 int_1^4 sqrt(y) "d"y`
= `12[(y^(3/2))/(3/2)]_1^4`
= `8[(4)^(3/2) - (1)^(3/2)]`
= 8(8 –1)
= 8(7)
= 56 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 ellipse `x^2/4 + y^2/9 = 1.`
Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line `x = a/sqrt2`
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
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`
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 of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.
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:
y = x2 + 1, x = 0, x = 3
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
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.
State whether the following is True or False :
The area bounded by the curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
State whether the following statement is True or False:
The area of portion lying below the X axis is negative
The area of the circle x2 + y2 = 16 is ______
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 of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
If a2 + b2 + c2 = – 2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, 1 + c^2x)|` then f(x) is a polynomial of degree
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 ______.
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
The figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.
Which strips are considered for the area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\]?
What is the area of an elementary horizontal strip of length \[x\] and infinitesimally small width \[dy\]?
Which standard form corresponds to a region bounded by the \[y\]-axis?
Why is the area enclosed by \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] written as \[4\int_0^a y\,dx\]?
