Advertisements
Advertisements
प्रश्न
Find the area of the region.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .
Advertisements
उत्तर
0 ≤ y ≤ x2 ; 0 ≤ y ≤ x + 2 ; -1 ≤ x ≤ 3
y = x2
y = x + 2
x2 = x + 2
x2 - x - 2 = 0
( x - 2 ) ( x + 1) = 0
⇒ x = - 1 , 2
∴ Required area is area of shaded portion
`Delta = int_(-1)^2 (Y_"line" - Y_"parabola" ) dx + int_2^3 Y_"line" dx`
`Delta = int_(-1)^2 ( x + 2 -x^2 ) dx + int_2^3 (x +2 ) dx`
`Delta = int_(-1)^2 [x^2/2 + 2x - x^3/3 ] + int_2^3 [ x^2/2 + 2x]`
`Delta = (2+ 4 - 8/3) - (1/2 - 2 + 1/3) + (9/2 + 6) - (2 + 4 ) `
`Delta = 10/3 + 2/3 +9/2`
`Delta = 4 + 9/2 = 17/2 ` Sq.units
APPEARS IN
संबंधित प्रश्न
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
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 of the region bounded by the parabola y2 = 16x and the line x = 4.
Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9 "at" (-1,2sqrt2)`.
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 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|`.
If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b 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.
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 ______
Find the area of the region bounded by the curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2
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
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.
The area bounded by the x-axis and the curve y = 4x – x2 – 3 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 ______.
