Advertisements
Advertisements
प्रश्न
The area of the region bounded by the circle x2 + y2 = 1 is ______.
विकल्प
2π sq.units
π sq.units
3π sq.units
4π sq.units
Advertisements
उत्तर
The area of the region bounded by the circle x2 + y2 = 1 is π sq.units.
Explanation:
Given equation of circle is x2 + y2 = 1
⇒ y = `sqrt(1 - x^2)`
Since the circle is symmetrical about the axes.
∴ Required area = `4 xx int_0^1 sqrt(1 - x^2) "d"x`
= `4[x/2 sqrt(1 - x^2) + 1/2 sin^-1 x]_0^1`
= `4[0 + 1/2 sin^-1 (1) - 0 - 0]`
= `4 xx 1/2 xx pi/2`
= π sq.units
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the curve x2 = 16y, lines y = 2, y = 6 and Y-axis lying in the first quadrant.
Using the method of integration find the area of the region bounded by lines: 2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0
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]
Sketch the graph of y = |x + 4|. Using integration, find the area of the region bounded by the curve y = |x + 4| and x = –6 and x = 0.
Find the area lying above the x-axis and under the parabola y = 4x − x2.
Draw a rough sketch of the graph of the curve \[\frac{x^2}{4} + \frac{y^2}{9} = 1\] and evaluate the area of the region under the curve and above the x-axis.
Sketch the region {(x, y) : 9x2 + 4y2 = 36} and find the area of the region enclosed by it, using integration.
Find the area of the region bounded by the curve \[x = a t^2 , y = 2\text{ at }\]between the ordinates corresponding t = 1 and t = 2.
Find the area bounded by the curve y = 4 − x2 and the lines y = 0, y = 3.
Find the area of the region \[\left\{ \left( x, y \right): \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 \leq \frac{x}{a} + \frac{y}{b} \right\}\]
Draw a rough sketch of the region {(x, y) : y2 ≤ 3x, 3x2 + 3y2 ≤ 16} and find the area enclosed by the region using method of integration.
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 region enclosed by the parabola x2 = y and the line y = x + 2.
Find the area of the region bounded by the curve y = \[\sqrt{1 - x^2}\], line y = x and the positive x-axis.
Find the area of the region enclosed between the two curves x2 + y2 = 9 and (x − 3)2 + y2 = 9.
Find the area of the region {(x, y): x2 + y2 ≤ 4, x + y ≥ 2}.
Find the area enclosed by the parabolas y = 4x − x2 and y = x2 − x.
If the area above the x-axis, bounded by the curves y = 2kx and x = 0, and x = 2 is \[\frac{3}{\log_e 2}\], then the value of k is __________ .
The area of the region bounded by the parabola (y − 2)2 = x − 1, the tangent to it at the point with the ordinate 3 and the x-axis is _________ .
The area bounded by the parabola y2 = 4ax and x2 = 4ay is ___________ .
The area bounded by the curve y = x4 − 2x3 + x2 + 3 with x-axis and ordinates corresponding to the minima of y 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 __________ .
The area bounded by the curve y = x |x| and the ordinates x = −1 and x = 1 is given by
Find the area of the region bounded by the parabola y2 = 2x and the straight line x – y = 4.
The area of the region bounded by the curve y = x2 + x, x-axis and the line x = 2 and x = 5 is equal to ______.
Find the area of the region bounded by the curve y = x3 and y = x + 6 and x = 0
Find the area of the region bounded by the curve y2 = 4x, x2 = 4y.
Find the area bounded by the curve y = `sqrt(x)`, x = 2y + 3 in the first quadrant and x-axis.
Find the area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5.
The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3 is ______.
The area of the region bounded by the curve x = 2y + 3 and the y lines. y = 1 and y = –1 is ______.
The curve x = t2 + t + 1,y = t2 – t + 1 represents
Let f(x) be a continuous function such that the area bounded by the curve y = f(x), x-axis and the lines x = 0 and x = a is `a^2/2 + a/2 sin a + pi/2 cos a`, then `f(pi/2)` =
Find the area bounded by the curve y = |x – 1| and y = 1, using integration.
Let T be the tangent to the ellipse E: x2 + 4y2 = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = `sqrt(5)` is `sqrt(5)`α + β + γ `cos^-1(1/sqrt(5))`, then |α + β + γ| is equal to ______.
The area of the region S = {(x, y): 3x2 ≤ 4y ≤ 6x + 24} is ______.
Find the area of the smaller region bounded by the curves `x^2/25 + y^2/16` = 1 and `x/5 + y/4` = 1, using integration.
