Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the following curves, X-axis and the given lines: xy = 2, x = 1, x = 4
उत्तर
For xy = 2, y = `(2)/x`.
Required area = `int_1^4 y*dx, "where" y = (2)/x`
= `int_1^4 (2)/x*dx`
= `[2 log |x|]_1^4`
= 2 log 4 – 2 log 1
= 2 log 4 – 0
= 2 log 4 sq units.
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the following curves, X-axis and the given lines: y = 2x, x = 0, x = 5
Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4
Find the area of the region bounded by the following curves, X-axis and the given lines : y = sin x, x = 0, x = `pi/(2)`
Find the area of the region included between y2 = 2x and y = 2x.
Choose the correct option from the given alternatives :
The area bounded by the curve y = x3, the X-axis and the lines x = – 2 and x = 1 is
Choose the correct option from the given alternatives :
The area of the region bounded between the line x = 4 and the parabola y2 = 16x is ______.
Choose the correct option from the given alternatives :
The area under the curve y = `2sqrt(x)`, enclosed between the lines x = 0 and x = 1 is
Choose the correct option from the given alternatives :
The area of the region bounded by the ellipse `x^2/a^2 + y^2/b^2` = 1 is
Choose the correct option from the given alternatives :
The area bounded by the parabola y2 = x and the line 2y = x is
Choose the correct option from the given alternatives :
The area enclosed between the curve y = cos 3x, 0 ≤ x ≤ `pi/(6)` and the X-axis is
Choose the correct option from the given alternatives :
The area bounded by y = `sqrt(x)` and the x = 2y + 3, X-axis in first quadrant is
Choose the correct option from the given alternatives :
The area bounded by the ellipse `x^2/a^2 y^2/b^2` = 1 and the line `x/a + y/b` = 1 is
Choose the correct option from the given alternatives :
The area of the region bounded by x2 = 16y, y = 1, y = 4 and x = 0 in the first quadrant, is
Choose the correct option from the given alternatives :
The area of the region included between the line x + y = 1 and the circle x2 + y2 = 1 is
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : 0 ≤ x ≤ 5, 0 ≤ y ≤ 2
Solve the following :
Find the area of the region lying between the parabolas : 4y2 = 9x and 3x2 = 16y
Solve the following :
Find the area enclosed between the circle x2 + y2 = 1 and the line x + y = 1, lying in the first quadrant.
The area of the region bounded by the ellipse x2/64 + y2/100 = 1, is ______ sq.units
The area bounded by the parabola y2 = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units
The area bounded by the parabola y2 = 32x the X-axis and the latus rectum is ______ sq.units
The area bounded by the ellipse `x^2/4 + y^2/25` = 1 and the line `x/2 + y/5` = 1 is ______ sq.units
Find the area of the region bounded by the parabola y2 = 32x and its Latus rectum in first quadrant
Find the area of the region bounded by the curve y = x2, the X−axis and the given lines x = 0, x = 3
Find the area of the region bounded by the curve y2 = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0
Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4
Find the area of the region bounded by the curves x2 = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant
Find the area of the region bounded by the curve y = sin x, the X−axis and the given lines x = − π, x = π
Find the area of the region bounded by the curves y2 = 4ax and x2 = 4ay
Find the area of the sector bounded by the circle x2+ y2 = 16, and the line y = x in the first quadrant
Find the area of the region bounded by the curve (y − 1)2 = 4(x + 1) and the line y = (x − 1)
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 2 and y = 4.
Find the area common to the parabola y2 = x – 3 and the line x = 5.
