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 the x-axis, the line y = x and the circle x2 + y2 = 32.
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
Find the area of the region bounded by the parabola y = x2 and y = |x| .
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 area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.
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
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 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 _______.
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
State whether the following is True or False :
The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy`
If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b 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 ______
State whether the following statement is True or False:
The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x) "d"x| + |int_"b"^"c" "f"(x) "d"x|`
Find the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Find the area of the circle x2 + y2 = 62
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
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 ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
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 included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
