Advertisements
Advertisements
Question
Find the area of the region included between: y2 = 4x, and y = x
Advertisements
Solution
The vertex of the parabola y2 = 4x is at the origin O = (0, 0).
Points of intersection of parabola and line are
∴ x2 = 4x
x2 = 4x = 0
∴ x(x - 4) = 0
x = 0 or x = 4
∴ y = x
points are (0, 0) & (4, 4)
Area bounded by parabola and line is = Area (OABCO)
= A (OCBCO) - A (OCBAO)
`int_0^4 2sqrtx*dx - int_0^4x*dx`
= `2 [x^(3/2)/(3/2)]_0^4 - [x^2/2]_0^4`
= `2 xx 2/3 [(4)^(3/2) - (0)^(3/2)] - 1/2 [4^2 - 0^2]`
= `4/3[8 - 0]- 1/2 [16 - 0]`
= `32/3 - 8`
= `(32 - 24)/3`
Area = `8/3` square units.
APPEARS IN
RELATED QUESTIONS
Find the area of the region bounded by the following curves, X-axis and the given lines : y = sin x, x = 0, x = `pi/(2)`
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 : 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: y = 4 – x2 and the X-axis.
Find the area of the region included between: y = x2 and the line y = 4x
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 bounded by the curve y = x3, the X-axis and the lines x = – 2 and x = 1 is
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 region bounded between the line x = 4 and the parabola y2 = 16x is ______.
Choose the correct option from the given alternatives :
The area under the curve y = `2sqrt(x)`, enclosed between the lines x = 0 and x = 1 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 parabola y2 = x and the line 2y = x is
Choose the correct option from the given alternatives :
The area bounded by the parabola y = x2 and the line y = x is
The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is ______.
Choose the correct option from the given alternatives :
The area of the region bounded by x2 = 16y, y = 1, y = 4 and x = 0 in the first quadrant, 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
Choose the correct option from the given alternatives :
The area of the region included between the line x + y = 1 and the circle x2 + y2 = 1 is
Solve the following :
Find the area of the region in first quadrant bounded by the circle x2 + y2 = 4 and the X-axis and the line x = `ysqrt(3)`.
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 = π
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 bounded by the curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).
Solve the following:
Find the area of the region bounded by the curve y = 4x2, Y-axis and the lines y = 1, y = 4.
The area of the region bounded by the ellipse x2/64 + y2/100 = 1, is ______ sq.units
The area bounded by the parabola y2 = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units
Find the area bounded by the curve y2 = 36x, the line x = 2 in first quadrant
Find the area bounded by the curve y = sin x, the lines x = 0 and x = `pi/2`
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
Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4
Find the area of the region bounded by the curves x2 = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant
Find the area of the region bounded by the curve y = sin x, the X−axis and the given lines x = − π, x = π
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 curve y = x3, the X-axis and the Lines x = –2 and x = 1 is ______.
Find the area of the region bounded by the curve y = x2 and the line y = 4.
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 bounded by the lines y = 5x – 10, X-axis and x = 5.
