मराठी

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`

Advertisements
Advertisements

प्रश्न

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`

Advertisements

उत्तर

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`, is represented by the shaded region BCAB as

∴ Area BCAB = Area (OBCAO) – Area (OBAO)

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 9 | पृष्ठ ३७५

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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 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 under the given curve and given line:

y = x4, x = 1, x = 5 and x-axis


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).


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


Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.


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


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 _______.


Using definite integration, area of the circle x2 + y2 = 49 is _______.


Fill in the blank :

Area of the region bounded by x2 = 16y, y = 1, 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 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` 


State whether the following is True or False :

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


Solve the following:

Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.


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:

Using the definite integration area of the circle x2 + y2 = 16 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 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|`


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 = (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 parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis


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


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


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 ____________.


Find the area between the two curves (parabolas)

y2 = 7x and x2 = 7y.


The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.


If the area enclosed by y = f(x), X-axis, x = a, x = b and y = g(x), X-axis, x = a, x = b are equal, then f(x) = g(x).


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.


Why cannot a curve crossing the \[x\]-axis within \[a,b\] be integrated directly from \[a\] to \[b\] to obtain total area?


For the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\], which expression for \[y\] is obtained before selecting the first-quadrant branch?


Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?


Which integral represents the enclosed area of the ellipse after using the positive first-quadrant value of \[y\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×