Advertisements
Advertisements
प्रश्न
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
Advertisements
उत्तर
The area of the region enclosed by the parabola, x2 = y, the line, y = x + 2, and x-axis is represented by the shaded region OACO as
The point of intersection of the parabola, x2 = y, and the line, y = x + 2, is A (–1, 1) and C(2, 4).
Area of OACO = ∫-12x + 2 dx - ∫-12 x2 dx⇒Area of OACO = x22 + 2x-12 - 13x3-12⇒Area of OACO = 222+22 - -122+2-1 - 1323 - -13⇒Area of OACO = 2 + 4 - 12-2 - 138 + 1⇒Area of OACO = 6 + 32 - 3⇒Area of OACO = 3 + 32 = 92 square 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 the ellipse `x^2/16 + y^2/9 = 1.`
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
Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`
Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b = 1`
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
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 = `sqrt(6x + 4), x = 0, x = 2`
Choose the correct alternative :
Area of the region bounded by the curve x2 = y, the X-axis and the lines x = 1 and x = 3 is _______.
Using definite integration, area of the circle x2 + y2 = 49 is _______.
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 _______.
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 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|`.
Solve the following :
Find the area of the region bounded by the curve y = x2 and the line y = 10.
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 ______
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 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`
The area of the region bounded by the curve y2 = x and the Y axis in the first quadrant and lines y = 3 and y = 9 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
The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 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 = ______
`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 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 included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
