English

Find the Area of the Region Bounded by the Curve Y2 = X and the Lines X = 1, X = 4 and the X-axis. - Mathematics

Advertisements
Advertisements

Question

Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.

Advertisements

Solution

The area of the region bounded by the curve, y2 = x, the lines, x = 1 and x = 4, and the x-axis is the area ABCD.

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Application of Integrals - Exercise 8.1 [Page 365]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 8 Application of Integrals
Exercise 8.1 | Q 1 | Page 365

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 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^2/16 + y^2/9 = 1.`


Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line  `x = a/sqrt2`


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


Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.


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


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


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


The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.


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


Fill in the blank :

The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 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 y = x2 and the line y = 10.


Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.


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 x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant 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 circle x2 + y2 = 16 is ______


The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant 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 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8


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


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


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


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


The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 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 included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is


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


Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis 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 figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×