Advertisements
Advertisements
Question
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Advertisements
Solution
The given equation of the curve is x2 = 25y.
∴ `5sqrt(y)` ...(∵ In first quadrant, x > 0)
Required area = `int_1^4x.dy`
∴ A = `int_1^4 5sqrt(y).dy`
∴ A = `5int_1^4 y^(1/2).dy`
∴ A = `5[(y^(3/2))/(3/2)]_1^4`
∴ A = `5 × 2/3 [4^(3/2) - 1]`
∴ A = `10/3 [(2^2)^(3/2) - 1]`
∴ A = `10/3 [8 - 1]`
∴ A = `10/3 × 7`
∴ A = `70/3` sq. units
APPEARS IN
RELATED QUESTIONS
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.
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
`x^2+y^2=4 at (1, sqrt3)`
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
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 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
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
Find the area of the region.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .
Find the area of the region bounded by the following curves, the X-axis and the given lines:
y = x2 + 1, x = 0, x = 3
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.
State whether the following is True or False :
The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy`
Choose the correct alternative:
Using the definite integration area of the circle x2 + y2 = 16 is ______
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 ______
The area of the circle x2 + y2 = 16 is ______
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
Find the area of the region bounded by the curve y = `sqrt(36 - x^2)`, the X-axis lying in the first quadrant and the lines x = 0 and x = 6
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
Area enclosed between the curve y2(4 - x) = x3 and line x = 4 above X-axis is ______.
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
If a2 + b2 + c2 = – 2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, 1 + c^2x)|` then f(x) is a polynomial of degree
The area included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) 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 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 ______.
Which strips are considered for the area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\]?
