Advertisements
Advertisements
प्रश्न
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.
उत्तर
Given equation of the curve is xy = c2
∴ y = `"c"^2/x`
∴ Required area = `int_"c"^(2"c") y*dx`
= `int_"c"^(2"c") "c"^2/x*dx`
= `"c"^2 int_"c"^(2c") (1/x)*dx`
= `"c"^2 [logx]_"c"^(2"c")`
= c2(log 2c – log c)
= `"c"^2 log ((2"c")/"c")`
= c2 log 2 sq.units.
APPEARS IN
संबंधित प्रश्न
The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
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 {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Fill in the blank :
Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant 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|`.
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 ______
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 is ______
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant 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 = 62
The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.
The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.
Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.
