Advertisements
Advertisements
Question
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
Advertisements
Solution
The region bounded by the parabola `y^2` = 16x and
the line x = 4 is the area OACO
The area OACO is symmetrical about x-axis
Area of OACO = 2(Area of OAB)
Area of OACO = `2int_0^4y dx`
=`2int_0^4 4sqrtx dx`
=`8[x^(3/2 )/(3/2)]_0^4`
=`16/3[x^(3/2)]_0^4`
=`16/3(8)=128/3`
Therefore, the required area is `128/3`sq. units.
APPEARS IN
RELATED QUESTIONS
Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line `x = a/sqrt2`
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 of the region bounded by the curve y2 = 4x and the line x = 3
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
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 \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4
Choose the correct alternative :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
State whether the following statement is True or False:
The area of portion lying below the X axis is negative
The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______
`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.
The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.
The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
If area of the region bounded by y ≥ cot( cot–1|In|e|x|) and x2 + y2 – 6 |x| – 6|y| + 9 ≤ 0, is λπ, then λ is ______.
The figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.
