Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Let A be the required area.
Given equation of the curve is y = `sqrt(36 - x^2)`
∴ A = `int_0^6 y "d"x`
= `int_0^6 sqrt(36 - x^2) "d"x`
= `int_0^6 sqrt((6)^2 + x^2) "d"x`
= `[x/2 sqrt((6)^2 - x^2) + (6)^2/2 sin^-1 (x/6)]_0^6`
= `[6/2 sqrt((6)^2 - (6)^2) + (6)^2/2 sin^-1 (6/6)] - [0/2 sqrt((6)^2 - 0) + (6)^2/2 sin^-1 (0/6)]`
= `0 + 36/2 sin^-1 (1) - 0`
= `36/2 (pi/2)`
= `(36pi)/4` sq.units
APPEARS IN
संबंधित प्रश्न
Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.
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 x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
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 y2 = 4ax and the line y = mx
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
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:
y = x2 + 1, x = 0, x = 3
Using definite integration, area of the circle x2 + y2 = 49 is _______.
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 y = x2 and the line y = 10.
Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______
State whether the following statement is True or False:
The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x) "d"x| + |int_"b"^"c" "f"(x) "d"x|`
The area of the circle x2 + y2 = 16 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 the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
Find the area of the circle x2 + y2 = 16
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
