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 x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
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`
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
Find the area of the region.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
Choose the correct alternative :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.
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 two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.
Solve the following :
Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.
Solve the following :
Find the area of the region bounded by the curve y = x2 and the line y = 10.
Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______
The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant 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
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 of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.
Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
The equation of curve through the point (1, 0), if the slope of the tangent to t e curve at any point (x, y) is `(y - 1)/(x^2 + x)`, is
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
The area bounded by the curve `y = 3/2sqrtx`, the line x = 1 and x-axis is ______ sq. units.
What is the area of an elementary horizontal strip of length \[x\] and infinitesimally small width \[dy\]?
Which expression gives physical area when the curve \[y=f(x)\] lies below the \[x\]-axis from \[x=a\] to \[x=b\]?
Which standard form corresponds to a region bounded by the \[y\]-axis?
