Advertisements
Advertisements
प्रश्न
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
विकल्प
63 sq. units
`(3)/(56)"sq. units"`
`(56)/(3)"sq. units"`
`(63)/(7)"sq. units"`
उत्तर
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is `bbunderline((56)/(3)"sq. units")`.
Explanation:
Required area = `int_1^4x*dy`
= `int_1^4 4sqrt(y)*dy`
= `4[y^(3/2)/(3/2)]_1^4`
= `(8)/(3)[(4)^(3/2) - (1)^(3/2)]`
= `(8)/(3)(8 - 1)`
= `(56)/(3)"sq.units"`.
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Choose the correct alternative :
Area of the region bounded by the curve x2 = y, the X-axis and the lines x = 1 and x = 3 is _______.
Using definite integration, area of the circle x2 + y2 = 49 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 _______.
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 ______
State whether the following statement is True or False:
The area of portion lying below the X axis is negative
The area of the region bounded by the curve y2 = x and the Y axis in the first quadrant and lines y = 3 and y = 9 is ______
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______
Find the area of the circle x2 + y2 = 16
The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
Area of the region bounded by y= x4, x = 1, x = 5 and the 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 ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
