हिंदी

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

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Application of Integrals - Exercise 8.1 [पृष्ठ ३६६]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 8 Application of Integrals
Exercise 8.1 | Q 11 | पृष्ठ ३६६

वीडियो ट्यूटोरियलVIEW ALL [3]

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.


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 y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.


Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`


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


Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`


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


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 equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`


Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]


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`


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


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|`.


State whether the following is True or False :

The area of the portion lying above the X-axis is positive.


Choose the correct alternative:

Using the definite integration area of the circle x2 + y2 = 16 is ______


State whether the following statement is True or False:

The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1


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


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 = 4y, the Y-axis lying in the first quadrant and the lines y = 3


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


Find the area of the circle x2 + y2 = 62 


The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______


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


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


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


Find the area between the two curves (parabolas)

y2 = 7x and x2 = 7y.


Area bounded by the curves y = `"e"^(x^2)`, the x-axis and the lines x = 1, x = 2 is given to be α square units. If the area bounded by the curve y = `sqrt(ℓ "n"x)`, the x-axis and the lines x = e and x = e4 is expressed as (pe4 – qe – α), (where p and q are positive integers), then (p + q) 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 ______.


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


The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m 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×