Advertisements
Advertisements
Question
Find the area of the region bounded by the curve y = x2, the X−axis and the given lines x = 0, x = 3
Solution
Let A be the required area.
Consider the equation y = x2 
∴ A = `int_0^3 y "d"x`
= `int_0^3 x^2 "d"x`
= `[x^3/3]_0^3`
= `1/3(3^3 - 0)`
= 9 sq.units
APPEARS IN
RELATED QUESTIONS
Find the area of the region bounded by the following curves, X-axis and the given lines : x = 0, x = 5, y = 0, y = 4
Find the area of the region bounded by the following curves, X-axis and the given lines: xy = 2, x = 1, x = 4
Find the area of the region bounded by the following curves, X-axis and the given lines : y2 = x, x = 0, x = 4
Find the area of the region bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4
Find the area of the region bounded by the parabola y2 = 16x and its latus rectum.
Find the area of the region included between y2 = 2x and y = 2x.
Find the area of the region included between: y2 = 4ax and the line y = x
Choose the correct option from the given alternatives :
The area bounded by the regional 1 ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by ______.
Choose the correct option from the given alternatives :
The area of the region enclosed by the curve y = `(1)/x`, and the lines x = e, x = e2 is given by
The area enclosed between the parabola y2 = 4x and line y = 2x is ______.
Choose the correct option from the given alternatives :
The area of the circle x2 + y2 = 25 in first quadrant is
Choose the correct option from the given alternatives :
The area bounded by the ellipse `x^2/a^2 y^2/b^2` = 1 and the line `x/a + y/b` = 1 is
Choose the correct option from the given alternatives :
The area bounded by the parabola y = x2 and the line y = x is
Choose the correct option from the given alternatives :
The area enclosed between the two parabolas y2 = 4x and y = x is
Choose the correct option from the given alternatives :
The area of the region included between the parabolas y2 = 4ax and x2 = 4ay, (a > 0) is given by
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : 0 ≤ x ≤ 5, 0 ≤ y ≤ 2
Solve the following :
Find the area of the region bounded by the parabola y2 = x and the line y = x in the first quadrant.
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = `pi/(3)`
Solve the following :
Find the area of the region lying between the parabolas : y2 = x and x2 = y.
Solve the following :
Find the area of the region bounded by the curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).
The area bounded by the parabola y2 = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units
The area bounded by the curve y2 = x2, and the line x = 8 is ______
The area enclosed by the line 2x + 3y = 6 along X-axis and the lines x = 0, x = 3 is ______ sq.units
Find the area of the region bounded by the curve y2 = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0
Find the area of the region bounded by the curve x2 = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 0
Find the area of the region bounded by the parabola x2 = 4y and The X-axis and the line x = 1, x = 4
Find the area of the sector bounded by the circle x2+ y2 = 16, and the line y = x in the first quadrant
Find the area of the region bounded by the curve y2 = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.
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 region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.
