English

Find the Area of the Region Bounded by the Curve Y2 = 4x And the Line X = 3 - Mathematics

Advertisements
Advertisements

Question

Find the area of the region bounded by the curve y2 = 4x and the line x = 3

Advertisements

Solution

The region bounded by the parabola, y2 = 4x, and the line, x = 3, is the area OACO.

The area OACO is symmetrical about x-axis.

∴ Area of OACO = 2 (Area of OAB)

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 11 | Page 366

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 x2 = 4yy = 2, y = 4 and the y-axis in the first quadrant.


The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.


Find the area under the given curve and given line:

y = x4, x = 1, x = 5 and x-axis


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


Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).


Find the area of the region. 

{(x,y) : 0 ≤ y ≤ x, 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 = `sqrt(16 - x^2)`, x = 0, x = 4


Choose the correct alternative :

Area of the region bounded by the curve x2 = y, the X-axis and the lines x = 1 and x = 3 is _______.


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


Using definite integration, area of the circle x2 + y2 = 49 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` 


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 x2 = 25y, y = 1, y = 4 and the Y-axis.


Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______


The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x)  "d"x`


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 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 = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2


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 the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2


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


If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?


Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.


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 ______.


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


The area of the region bounded by the curve y = x2, x = 0, x = 3, and the X-axis is ______.


The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] 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 area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×