Advertisements
Advertisements
प्रश्न
The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is ______.
पर्याय
8 sq.units
20π sq.units
16π sq.units
256π sq.units
Advertisements
उत्तर
The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is 8 sq.units.
Explanation:
Here, equation of curve is y = `sqrt(16 - x^2)`
Required area = `2[int_0^4 sqrt(16 - x^2) "d"x]`
= `2[x/2 sqrt(16 - x^2) + 16/2 sin^-1 x/4]_0^4`
= `2[(0 + 8 sin^-1 4/4) - (0 + 0)]`
= `2[8sin^-1 (1)]`
= `16 * pi/2`
= 8 sq.units.
APPEARS IN
संबंधित प्रश्न
Using integration, find the area bounded by the curve x2 = 4y and the line x = 4y − 2.
Sketch the region bounded by the curves `y=sqrt(5-x^2)` and y=|x-1| and find its area using integration.
Find the area bounded by the curve y = sin x between x = 0 and x = 2π.
Find the equation of a curve passing through the point (0, 2), given that the sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at that point by 5.
Determine the area under the curve y = `sqrt(a^2-x^2)` included between the lines x = 0 and x = a.
Show that the areas under the curves y = sin x and y = sin 2x between x = 0 and x =\[\frac{\pi}{3}\] are in the ratio 2 : 3.
Find the area of the minor segment of the circle \[x^2 + y^2 = a^2\] cut off by the line \[x = \frac{a}{2}\]
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.
Prove that the area common to the two parabolas y = 2x2 and y = x2 + 4 is \[\frac{32}{3}\] sq. units.
Using the method of integration, find the area of the region bounded by the following lines:
3x − y − 3 = 0, 2x + y − 12 = 0, x − 2y − 1 = 0.
Find the area bounded by the parabola x = 8 + 2y − y2; the y-axis and the lines y = −1 and y = 3.
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 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 __________ .
Sketch the graphs of the curves y2 = x and y2 = 4 – 3x and find the area enclosed between them.
Find the area of the curve y = sin x between 0 and π.
The area enclosed by the circle x2 + y2 = 2 is equal to ______.
The area enclosed by the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 is equal to ______.
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 region bounded by the line x = 2 and the parabola y2 = 8x
Using integration, find the area of the region bounded by the line 2y = 5x + 7, x- axis and the lines x = 2 and x = 8.
Find the area of the region bounded by the curve y2 = 2x and x2 + y2 = 4x.
Draw a rough sketch of the region {(x, y) : y2 ≤ 6ax and x 2 + y2 ≤ 16a2}. Also find the area of the region sketched using method of integration.
Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.
The area of the region bounded by the curve y = sinx between the ordinates x = 0, x = `pi/2` and the x-axis is ______.
The area of the region bounded by the ellipse `x^2/25 + y^2/16` = 1 is ______.
Area of the region bounded by the curve `y^2 = 4x`, `y`-axis and the line `y` = 3 is:
Find the area of the region bounded by the curve `y^2 - x` and the line `x` = 1, `x` = 4 and the `x`-axis.
What is the area of the region bounded by the curve `y^2 = 4x` and the line `x` = 3.
Find the area of the region bounded by curve 4x2 = y and the line y = 8x + 12, using integration.
Let the curve y = y(x) be the solution of the differential equation, `("dy")/("d"x) = 2(x + 1)`. If the numerical value of area bounded by the curve y = y(x) and x-axis is `(4sqrt(8))/3`, then the value of y(1) is equal to ______.
The area (in sq.units) of the region A = {(x, y) ∈ R × R/0 ≤ x ≤ 3, 0 ≤ y ≤ 4, y ≤x2 + 3x} is ______.
The area (in square units) of the region bounded by the curves y + 2x2 = 0 and y + 3x2 = 1, is equal to ______.
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.
Find the area of the minor segment of the circle x2 + y2 = 4 cut off by the line x = 1, using integration.
Find the area of the region bounded by the curve x2 = 4y and the line x = 4y – 2.
