Advertisements
Advertisements
Question
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Advertisements
Solution
Given equation of the parabola is y2 = 4x
∴ `y = 2sqrt(x)` ...[∵ In first quadrant, y > 0]
And equation of the line is x = 3
∴ Required = Area of the region OQRPO
= 2(Area of the region ORPO)
= `2 int_0^3y.dx`
= `2 int_0^3 2sqrt(x).dx`
= `4 int_0^3 sqrt(x).dx`
= `4 int_0^3 x^(1/2).dx`
= `4[(x^(3/2))/(3/2)]_0^3`
= `4 xx (2)/(3)[(3)^(3/2) - 0]`
= `8/3(3sqrt(3))`
∴ Required area = `8sqrt(3)` sq. units.
APPEARS IN
RELATED QUESTIONS
Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
Choose the correct alternative:
Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______
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|`
State whether the following statement is True or False:
The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis 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 area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 is ______
The area included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
The area of the region bounded by the curve y = x2, x = 0, x = 3, and the X-axis is ______.
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.
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 area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis 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 ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
What is the area of an elementary horizontal strip of length \[x\] and infinitesimally small width \[dy\]?
Which integral gives the area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\]?
