Advertisements
Advertisements
Question
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
Advertisements
Solution
Given equation of the parabola is y2 = 25x
∴ y = `5sqrt(x)` ......[∵ In first quadrant, y > 0]
Required area = area of the region OQRPO
= 2 (area of the region ORPO)
= `2 int_0^5 y "d"x`
= `2 int_0^5 5sqrt(x) "d"x`
= `10 int_0^5 x^(1/2) "d"x`
= `10[(x^(3/2))/(3/2)]_0^5`
= `20/5[(5)^(3/2) - 0]`
= `20/3 (5sqrt(5))`
= `(100sqrt(5))/3` sq.units
APPEARS IN
RELATED QUESTIONS
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
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.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .
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: 2y + x = 8, x = 2, x = 4
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Choose the correct alternative:
Using the definite integration area of the circle x2 + y2 = 16 is ______
The area of the circle x2 + y2 = 16 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 ______
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
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 ______
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
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 ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
What is the total area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\], when the region is above the \[x\]-axis?
For an area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\], which strips are used?
Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?
