Advertisements
Advertisements
Question
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
Advertisements
Solution
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
RELATED QUESTIONS
Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.
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 y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
Find the area of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
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 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^2/9 + y^2/4` and the line `x/3 + y/2 = 1`
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 of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 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.
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
State whether the following statement is True or False:
The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x) "d"x| + |int_"b"^"c" "f"(x) "d"x|`
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 y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
Find the area of the circle x2 + y2 = 62
Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.
The area included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
For an area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\], which strips are used?
A curve crosses the \[x\]-axis, forming area \[A_1\] below the axis and area \[A_2\] above the axis. What is its total area?
What is the area enclosed by the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
