Advertisements
Advertisements
Question
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Advertisements
Solution
Given equation of the parabola is y2 = 4x
∴ `y = 2sqrt(x)` ...[∵ In first quadrant, y > 0]
And equation of the line is x = 3
∴ Required = Area of the region OQRPO
= 2(Area of the region ORPO)
= `2 int_0^3y.dx`
= `2 int_0^3 2sqrt(x).dx`
= `4 int_0^3 sqrt(x).dx`
= `4 int_0^3 x^(1/2).dx`
= `4[(x^(3/2))/(3/2)]_0^3`
= `4 xx (2)/(3)[(3)^(3/2) - 0]`
= `8/3(3sqrt(3))`
∴ Required area = `8sqrt(3)` sq. units.
APPEARS IN
RELATED QUESTIONS
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
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(6x + 4), x = 0, x = 2`
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y = 5x + 7, x = 2, x = 8
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 _______.
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`
The area of the circle x2 + y2 = 16 is ______
The area of the region lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 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 parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5
The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______
Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.
The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
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 slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.
Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.
For an area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\], which strips are used?
Why is the area enclosed by \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] written as \[4\int_0^a y\,dx\]?
