English

Find the Area Bounded by the Curve X2 = 4y and the Line X = 4y – 2

Advertisements
Advertisements

Question

Find the area bounded by the curve x2 = 4y and the line x = 4– 2

Advertisements

Solution

The area bounded by the curve, x2 = 4y, and line, x = 4– 2, is represented by the shaded area OBAO.

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Application of Integrals - Exercise 8.1 [Page 366]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 8 Application of Integrals
Exercise 8.1 | Q 10 | Page 366

RELATED QUESTIONS

Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.


Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`


Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).


Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.


Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.


Find the area of the region bounded by the parabola y2 = 16x and the line x = 4. 


Find the area of the region bounded by the following curves, the X-axis, and the given lines:

y = `sqrt(6x + 4), x = 0, x = 2`


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


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 _______.


State whether the following is True or False :

The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.


If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.


Solve the following :

Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.


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|`


Find the area of the region bounded by the parabola y2 = 25x and the line x = 5


Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3


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


Find the area of the circle x2 + y2 = 16


The area of the region bounded by the curve y = 4x3 − 6x2 + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.


The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.


The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 is ______ 


`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.


Area enclosed between the curve y2(4 - x) = x3 and line x = 4 above X-axis is ______.


The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.


Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.


The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 is ______.


Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:


The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`


The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) 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 | x | + y = 1 and X-axis is ______.


The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.


Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.


The area bounded by the curve `y = 3/2sqrtx`, the line x = 1 and x-axis is ______ sq. units.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×