Advertisements
Advertisements
प्रश्न
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
विकल्प
28 sq. units
3 sq. units
`(28)/(3)` sq. units
`(3)/(28)` sq. units
Advertisements
उत्तर
`bb((28)/(3))` sq. units
Explanation:
The right-handed parabola in this example, y2 = 4x, has its vertex at the origin, and the lines parallel to the y-axis at x = 1 to x = 4 units distance are x = 1, x = 4.
Similarly y2 = 4x contains even power of y and is symmetrical about the x-axis.
So the required area = Area of ABCD
Area of ABCD = `int_1^4ydx=int_1^4sqrt(4x)dx`
It can be written as
= `2int_1^4sqrtxdx`
= `2[(x3/2)/(3/2)]_1^4`
= `2[(2x3/2)/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
Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32.
Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.
Find the area of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
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/a^2 + y^2/b^2 = 1` and the line `x/a + y/b = 1`
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 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 following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4
Choose the correct alternative :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.
Using definite integration, area of the circle x2 + y2 = 49 is _______.
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
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 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 curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
If a2 + b2 + c2 = – 2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, 1 + c^2x)|` then f(x) is a polynomial of degree
The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
