मराठी

The Area Between X = Y2 And X = 4 is Divided into Two Equal Parts by the Line X = A, Find the Value Of A. - Mathematics

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

The line, x = a, divides the area bounded by the parabola and x = 4 into two equal parts.

∴ Area OAD = Area ABCD

It can be observed that the given area is symmetrical about x-axis.

⇒ Area OED = Area EFCD

From (1) and (2), we obtain

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Application of Integrals - Exercise 8.1 [पृष्ठ ३६६]

APPEARS IN

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

व्हिडिओ 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 under the given curve and given line:

y = x4, x = 1, x = 5 and x-axis


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^2/9 + y^2/4` and the line `x/3 + y/2 = 1`


Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.


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:  2y = 5x + 7, x = 2, x = 8


Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4


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


Choose the correct alternative :

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


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 xy = c2, the X-axis, and the lines x = c, x = 2c.


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 y2 = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant 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|`


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


Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8


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


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 ____________.


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


`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.


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 ______.


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


Find the area between the two curves (parabolas)

y2 = 7x and x2 = 7y.


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 ______.


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 ______.


Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis 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×