Advertisements
Advertisements
प्रश्न
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
पर्याय
`pi`
`pi/2`
`pi/3`
`pi/4`
Advertisements
उत्तर
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is π.
Explanation:
Equation of a circle x2 + y2 = 4
Required ocean = Ocean of OAB
`= int_0^2 y dx`
`= int_0^2 sqrt(4 - x^2) dx [(because x^2 + y^2 = 4),(=> y = sqrt(4 - x^2))]`
`= [x/2 sqrt(4 - x^2) + 4/2 sin^-1 x/2]_0^2`
`= [0 + 2 sin^-1 (1)] - (0 + 0)`
`= 2 xx pi/2`
= π Units
APPEARS IN
संबंधित प्रश्न
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
`x^2+y^2=4 at (1, sqrt3)`
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
Find the area of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
Find the area between the curves y = x and y = x2
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 by the parabola 4y = 3x2 and the line 2y = 3x + 12
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
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: 2y = 5x + 7, x = 2, x = 8
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
Choose the correct alternative :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.
State whether the following is True or False :
The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.
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|`.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______
Choose the correct alternative:
Area of the region bounded by y2 = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant is ______
Choose the correct alternative:
Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant 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`
Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Find the area of the region bounded by the curve y = `sqrt(36 - x^2)`, the X-axis lying in the first quadrant and the lines x = 0 and x = 6
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 ____________.
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
Area enclosed between the curve y2(4 - x) = x3 and line x = 4 above X-axis is ______.
The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 is ______.
The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
If the area enclosed by y = f(x), X-axis, x = a, x = b and y = g(x), X-axis, x = a, x = b are equal, then f(x) = g(x).
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
