Advertisements
Advertisements
प्रश्न
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
Advertisements
उत्तर
The area of the region bounded by the circle, `x^2 + y^2 = 4, x = sqrt3` and the x-axis is the area OAB.
The point of intersection of the line and the circle in the first quadrant is .`(sqrt3,1)`
Area OAB = Area ΔOCA + Area ACB
Therefore, required area enclosed = 32 + π3 - 32 = π3 square units
APPEARS IN
संबंधित प्रश्न
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 of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 1 and y = 4
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
Find the area of the region.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 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: 2y + x = 8, x = 2, x = 4
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
Find the area of the region bounded by the following curve, the X-axis and the given line:
y = 2 – x2, x = –1, x = 1
State whether the following is True or False :
The area bounded by the curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
Solve the following :
Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Choose the correct alternative:
Using the definite integration area of the circle x2 + y2 = 16 is ______
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
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 bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______
The area of the region lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 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 of the circle x2 + y2 = 16
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
The area of the region bounded by the curve y = 4x3 − 6x2 + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
The equation of curve through the point (1, 0), if the slope of the tangent to t e curve at any point (x, y) is `(y - 1)/(x^2 + x)`, is
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
Which strips are considered for the area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\]?
What is the total area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\], when the region is above the \[x\]-axis?
For an area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\], which strips are used?
What is the area of an elementary horizontal strip of length \[x\] and infinitesimally small width \[dy\]?
Which integral gives the area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\]?
Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?
What is the area enclosed by the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
