Advertisements
Advertisements
प्रश्न
The area enclosed by the circle x2 + y2 = 2 is equal to ______.
विकल्प
4π sq.units
`2sqrt(2)pi` sq.units
4π2 sq.units
2π sq.units
उत्तर
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
संबंधित प्रश्न
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.
Draw a rough sketch of the curve and find the area of the region bounded by curve y2 = 8x and the line x =2.
Draw the rough sketch of y2 + 1 = x, x ≤ 2. Find the area enclosed by the curve and the line x = 2.
Draw a rough sketch of the graph of the function y = 2 \[\sqrt{1 - x^2}\] , x ∈ [0, 1] and evaluate the area enclosed between the curve and the x-axis.
Compare the areas under the curves y = cos2 x and y = sin2 x between x = 0 and x = π.
Using integration, find the area of the triangle ABC coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4).
Using integration find the area of the region:
\[\left\{ \left( x, y \right) : \left| x - 1 \right| \leq y \leq \sqrt{5 - x^2} \right\}\]
Find the area of the circle x2 + y2 = 16 which is exterior to the parabola y2 = 6x.
Using integration, find the area of the following region: \[\left\{ \left( x, y \right) : \frac{x^2}{9} + \frac{y^2}{4} \leq 1 \leq \frac{x}{3} + \frac{y}{2} \right\}\]
Find the area enclosed by the curves y = | x − 1 | and y = −| x − 1 | + 1.
If the area bounded by the parabola \[y^2 = 4ax\] and the line y = mx is \[\frac{a^2}{12}\] sq. units, then using integration, find the value of m.
Find the area of the region bounded by the parabola y2 = 2x and the straight line x − y = 4.
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 curve y = x4 − 2x3 + x2 + 3 with x-axis and ordinates corresponding to the minima of y is _________ .
The closed area made by the parabola y = 2x2 and y = x2 + 4 is __________ .
Area bounded by the curve y = x3, the x-axis and the ordinates x = −2 and x = 1 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 bound by the curves y = 6x – x2 and y = x2 – 2x
Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.
Using integration, find the area of the region bounded between the line x = 4 and the parabola y2 = 16x.
The region bounded by the curves `x = 1/2, x = 2, y = log x` and `y = 2^x`, then the area of this region, is
Find the area of the region bounded by `y^2 = 9x, x = 2, x = 4` and the `x`-axis in the first quadrant.
The area enclosed by y2 = 8x and y = `sqrt(2x)` that lies outside the triangle formed by y = `sqrt(2x)`, x = 1, y = `2sqrt(2)`, is equal to ______.
Let f : [–2, 3] `rightarrow` [0, ∞) be a continuous function such that f(1 – x) = f(x) for all x ∈ [–2, 3]. If R1 is the numerical value of the area of the region bounded by y = f(x), x = –2, x = 3 and the axis of x and R2 = `int_-2^3 xf(x)dx`, then ______.
Let g(x) = cosx2, f(x) = `sqrt(x)`, and α, β (α < β) be the roots of the quadratic equation 18x2 – 9πx + π2 = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = α, x = β and y = 0, is ______.
Find the area of the following region using integration ((x, y) : y2 ≤ 2x and y ≥ x – 4).
Using integration, find the area of the region bounded by y = mx (m > 0), x = 1, x = 2 and the X-axis.
Sketch the region enclosed bounded by the curve, y = x |x| and the ordinates x = −1 and x = 1.
