मराठी

Find the Area Between the Curves Y = X and Y = X2 - Mathematics

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

The required area is represented by the shaded area OBAO as

The points of intersection of the curves, y = x and y = x2, is A (1, 1).

We draw AC perpendicular to x-axis.

∴ Area (OBAO) = Area (ΔOCA) – Area (OCABO) … (1)

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Application of Integrals - Exercise 8.3 [पृष्ठ ३७५]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 8 Application of Integrals
Exercise 8.3 | Q 2 | पृष्ठ ३७५

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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


Find the area of the region bounded by the ellipse  `x^2/16 + 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 = 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


Find the area enclosed between the parabola y2 = 4ax and the line y mx


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`


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


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`


Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9  "at" (-1,2sqrt2)`.


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:  2y = 5x + 7, x = 2, x = 8


Find the area of the region bounded by the following curve, the X-axis and the given line:

y = 2 – x2, x = –1, x = 1


Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant 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|`.


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 ______


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 lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 is ______


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 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


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


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


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 ______.


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


Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.


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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×