Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the curve y2 = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.
उत्तर
Let A be the required area.
A = `int_1^4 y dx`
= `int_1^4 2sqrt(x) dx`
= `2 int_1^4 x^(1/2) dx`
= `2 . 2/3 [x^(3/2)]_1^4`
= `4/3 [4^(3/2) - 1]`
A = `28/3` 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 : y = sin x, x = 0, x = `pi/(2)`
Find the area of the region bounded by the following curves, X-axis and the given lines : x = 0, x = 5, y = 0, y = 4
Find the area of the region bounded by the following curves, X-axis and the given lines : y2 = x, x = 0, x = 4
Find the area of the region bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4
Find the area of the region bounded by the parabola y2 = 16x and its latus rectum.
Find the area of the region included between: y = x2 and the line y = 4x
Choose the correct option from the given alternatives :
The area bounded by the regional 1 ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by ______.
Choose the correct option from the given alternatives :
The area of the region enclosed by the curve y = `(1)/x`, and the lines x = e, x = e2 is given by
The area of the region bounded by y = cos x, Y-axis and the lines x = 0, x = 2π is ______.
Choose the correct option from the given alternatives :
The area bounded by the parabola y2 = 8x, the X-axis and the latus rectum 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
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π
Solve the following :
Find the area of the region lying between the parabolas : 4y2 = 9x and 3x2 = 16y
Solve the following :
Find the area of the region lying between the parabolas : y2 = x and x2 = y.
Solve the following :
Find the area enclosed between the circle x2 + y2 = 1 and the line x + y = 1, lying in the first quadrant.
Solve the following :
Find the area of the region bounded by the curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).
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 curve y2 = x2, and the line x = 8 is ______
The area enclosed by the line 2x + 3y = 6 along X-axis and the lines x = 0, x = 3 is ______ sq.units
Find the area bounded by the curve y2 = 36x, the line x = 2 in first quadrant
Find the area of the region bounded by the curve x2 = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 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 parabola x2 = 4y and The X-axis and the line x = 1, x = 4
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4
Find the area of the region bounded by the curves y2 = 4ax and x2 = 4ay
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.
Find the area bounded by the lines y = 5x – 10, X-axis and x = 5.
Find the area of the region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.
