Advertisements
Advertisements
प्रश्न
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
उत्तर
Let A be the required area.
Consider the equation y = x2 + 1
∴ A = `int_0^3 y.dx`
= `int_0^3 (x^2 + 1).dx`
= `[x^3/3 + x]_0^3`
= `[3/3 + 3 - (0^3/3 + 0)]`
= `27/3 + 3 - 0`
= 9 + 3
∴ A = 12 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)`
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
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`
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
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 = `sqrt(6x + 4), x = 0, x = 2`
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
Choose the correct alternative :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.
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.
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 the curve x2 = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 is ______
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 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
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 ______
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
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 ______.
The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
