English

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

Advertisements
Advertisements

Question

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

Solution

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
  Is there an error in this question or solution?
Chapter 8: Application of Integrals - Exercise 8.3 [Page 375]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 8 Application of Integrals
Exercise 8.3 | Q 2 | Page 375

RELATED QUESTIONS

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


Find the area under the given curve and given line:

y = x4, x = 1, x = 5 and x-axis


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. 

{(x,y) : 0 ≤ y ≤ x, 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .


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 + x = 8, x = 2, 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


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


Choose the correct alternative :

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 y = x4, x = 1, x = 5 and the X-axis is _______.


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


Solve the following :

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


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 area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3


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


`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______ 


Area enclosed between the curve y2(4 - x) = x3 and line x = 4 above X-axis is ______.


The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.


Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.


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


Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?


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


The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.


Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 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 (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.


The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 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×