Advertisements
Advertisements
Question
The area enclosed by the circle x2 + y2 = 2 is equal to ______.
Options
4π sq.units
`2sqrt(2)pi` sq.units
4π2 sq.units
2π sq.units
Solution
The area enclosed by the circle x2 + y2 = 2 is equal to 2π sq units.
Explanation:
Since Area = `4int_0^sqrt(2) sqrt(2 - x^2)`
= `4(x/2 sqrt(2 - x^2) + sin^-1 x/sqrt(2))_0^sqrt(2)`
= 2π sq.units
APPEARS IN
RELATED QUESTIONS
Find the area of the region bounded by the curve y = sinx, the lines x=-π/2 , x=π/2 and X-axis
Using integration, find the area bounded by the curve x2 = 4y and the line x = 4y − 2.
Prove that the curves y2 = 4x and x2 = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.
The area bounded by the curve y = x | x|, x-axis and the ordinates x = –1 and x = 1 is given by ______.
[Hint: y = x2 if x > 0 and y = –x2 if x < 0]
Find the area of the region lying in the first quandrant bounded by the curve y2= 4x, X axis and the lines x = 1, x = 4
Draw a rough sketch of the curve and find the area of the region bounded by curve y2 = 8x and the line x =2.
Sketch the region {(x, y) : 9x2 + 4y2 = 36} and find the area of the region enclosed by it, using integration.
Sketch the graph y = | x + 1 |. Evaluate\[\int\limits_{- 4}^2 \left| x + 1 \right| dx\]. What does the value of this integral represent on the graph?
Find the area of the region bounded by y =\[\sqrt{x}\] and y = x.
Find the area of the region common to the circle x2 + y2 = 16 and the parabola y2 = 6x.
Draw a rough sketch of the region {(x, y) : y2 ≤ 5x, 5x2 + 5y2 ≤ 36} and find the area enclosed by the region using method of integration.
Make a sketch of the region {(x, y) : 0 ≤ y ≤ x2 + 3; 0 ≤ y ≤ 2x + 3; 0 ≤ x ≤ 3} and find its area using integration.
Find the area of the region enclosed between the two curves x2 + y2 = 9 and (x − 3)2 + y2 = 9.
Find the area enclosed by the curves y = | x − 1 | and y = −| x − 1 | + 1.
Find the area of the figure bounded by the curves y = | x − 1 | and y = 3 −| x |.
The area bounded by y = 2 − x2 and x + y = 0 is _________ .
If An be the area bounded by the curve y = (tan x)n and the lines x = 0, y = 0 and x = π/4, then for x > 2
The area bounded by the parabola y2 = 4ax, latusrectum and x-axis is ___________ .
The area bounded by the curve y = f (x), x-axis, and the ordinates x = 1 and x = b is (b −1) sin (3b + 4). Then, f (x) is __________ .
Using integration, find the area of the region bounded by the line x – y + 2 = 0, the curve x = \[\sqrt{y}\] and y-axis.
Find the area of the region bounded by the parabola y2 = 2px, x2 = 2py
Find the area of the region bounded by the curve y2 = 4x, x2 = 4y.
The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is ______.
The area of the region bounded by the ellipse `x^2/25 + y^2/16` = 1 is ______.
The area of the region bounded by the circle x2 + y2 = 1 is ______.
Area of the region bounded by the curve `y^2 = 4x`, `y`-axis and the line `y` = 3 is:
For real number a, b (a > b > 0),
let Area `{(x, y): x^2 + y^2 ≤ a^2 and x^2/a^2 + y^2/b^2 ≥ 1}` = 30π
Area `{(x, y): x^2 + y^2 ≥ b^2 and x^2/a^2 + y^2/b^2 ≤ 1}` = 18π.
Then the value of (a – b)2 is equal to ______.
Using integration, find the area of the region bounded by y = mx (m > 0), x = 1, x = 2 and the X-axis.
Find the area of the region bounded by the curve x2 = 4y and the line x = 4y – 2.
