English

Find the Area of the Region {(X, Y) : Y2 ≤ 4x, 4x2 + 4y2 ≤ 9}

Advertisements
Advertisements

Question

Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}

Advertisements

Solution

The area bounded by the curves, {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}, is represented as

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Application of Integrals - Exercise 8.3 [Page 376]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 8 Application of Integrals
Exercise 8.3 | Q 15 | Page 376

RELATED QUESTIONS

Using integration find the area of the region {(x, y) : x2+y2 2ax, y2 ax, x, y  0}.


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 in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.


Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line  `x = a/sqrt2`


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


Find the area between the curves y = x and y = x2


Find the area of the region lying in the first quadrant and bounded by y = 4x2x = 0, y = 1 and = 4


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 integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.


Find the area of the region bounded by the following curves, the X-axis and the given lines:  y = x4, x = 1, x = 5


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`


Choose the correct alternative :

Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis 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 _______.


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 ______


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 ______


Choose the correct alternative:

Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______


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 ______


The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 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 ______


The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______


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 y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3


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


Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant


Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2


Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis


Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5


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


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


Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?


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


The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.


The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.


The area bounded by the curve | x | + y = 1 and X-axis is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×