Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32.
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 1 and y = 4
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
Fill in the blank :
Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.
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 the curve y = x3, x = 1, x = 4 and the X-axis is ______
Choose the correct alternative:
Area of the region bounded by the curve x2 = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 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|`
The area of the circle x2 + y2 = 16 is ______
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 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8
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
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.
The equation of curve through the point (1, 0), if the slope of the tangent to t e curve at any point (x, y) is `(y - 1)/(x^2 + x)`, is
Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.
The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.
What is the area of an arbitrary elementary vertical strip of height \[y\] and width \[dx\]?
Which strips are considered for the area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\]?
