Advertisements
Advertisements
प्रश्न
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
Advertisements
उत्तर
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is `underlinebb(28/3)` sq. units.
Required area = `2int_1^4y*dx`
= `2int_1^4 2sqrt(x)*dx`
= `2[x^(3/2)/(3/2)]_1^4`
= `2[(2x^(3/2))/(3)]_1^4`
Substituting the values we get
= `2 = ((2(4)^(3/2))/3 - (2(1)^(3/2))/3)`
= `4 (8/3 - 1/3)`
= `4 (7/3)`
= `28/3` 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 curve y2 = x and the lines x = 1, x = 4 and the x-axis.
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 under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
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 \[\frac{x}{3} + \frac{y}{2} = 1 .\]
Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9 "at" (-1,2sqrt2)`.
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
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 :
Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.
Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______
Choose the correct alternative:
Area of the region bounded by y2 = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant is ______
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
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 ______
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
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 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 ______.
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 ______.
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
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 ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
If the area enclosed by y = f(x), X-axis, x = a, x = b and y = g(x), X-axis, x = a, x = b are equal, then f(x) = g(x).
What is the area of an arbitrary elementary vertical strip of height \[y\] and width \[dx\]?
Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
