Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3
Advertisements
उत्तर
Let A be the required area.
Given equation of the curve is y = (x2 + 2)2
∴ A = `int_1^3 y "d"x`
= `int_1^3 (x^2 + 2)^2 "d"x`
= `int_0^3 (x^4 + 4x^2 + 4)`
= `[x^5/5 + 4(x^3/3) + 4x]_1^3`
= `[3^5/5 + 4(3^3/3) + 4(3)] - [1^5/5 + 4(1^3/3) + 4(1)]`
= `(243/5 + 36 + 12) - (1/5 + 4/3 + 4)`
= `483/5 - 83/15`
= `(1449 - 83)/15`
= `1366/15` sq.units
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)`
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
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 parabola y2 = 16x and the line x = 4.
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: y = `sqrt(16 - x^2)`, x = 0, x = 4
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 curve, the X-axis and the given line:
y = 2 – x2, x = –1, x = 1
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
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 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 statement is True or False:
The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8
Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5
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 bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
