Advertisements
Advertisements
Question
Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3
Advertisements
Solution
Let A be the required area.
Given equation of the curve is y = `sqrt(9 - x^2)`
∴ A = `int_0^3 y "d"x`
= `int_0^3 sqrt(9 - x^2) "d"x`
= `int_0^3 sqrt((3)^2 - x^2) "d"x`
= `[x/2 sqrt((3)^2 - x^2) + (3)^2/2 sin^-1 (x/3)]_0^3`
= `[3/2 sqrt((3)^2 - (3)^2) + (3)^2/2 sin^-1 (3/3)] - [0/2 sqrt((3)^2 - 0^2) + (3)^2/2 sin^-1 (0/3)]`
= `0 + 9/2 sin^-1 (1) - 0`
= `9/2 (pi/2)`
∴ A = `(9pi)/4` sq.units
RELATED QUESTIONS
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 = x2, x = 1, x = 2 and x-axis
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 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(2, 0), B (4, 5) and C (6, 3).
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
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
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
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 _______.
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`
Choose the correct alternative:
Area of the region bounded by the curve x2 = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 is ______
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
State whether the following statement is True or False:
The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1
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 region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 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 ______
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______
Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant
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 ______.
The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, 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 x-axis and the curve y = 4x – x2 – 3 is ______.
The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
