English

Solve the following : Find the area of the region bounded by the following curve, the X-axis and the given lines : (i) 0 ≤ x ≤ 5, 0 ≤ y ≤ 2(ii) y = sin x, x = 0, x = π(iii) y = sin x, x = 0, x = π3. - Mathematics and Statistics

Advertisements
Advertisements

Question

Solve the following :

Find the area of the region bounded by the following curve, the X-axis and the given lines : 0 ≤ x ≤ 5, 0 ≤ y ≤ 2

Sum
Advertisements

Solution

Required area = `int_0^5 y*dx,  "where"  y = 2`

= `int_0^5 2*dx = [2x]_0^5`

= 2 x 5 – 0
= 10 sq units.

shaalaa.com
Area Bounded by the Curve, Axis and Line
  Is there an error in this question or solution?
Chapter 5: Application of Definite Integration - Miscellaneous Exercise 5 [Page 190]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 5 Application of Definite Integration
Miscellaneous Exercise 5 | Q 2.01 | Page 190

RELATED QUESTIONS

Find the area of the region bounded by the following curves, X-axis and the given lines: y = 2x, x = 0, x = 5


Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4


Find the area of the region bounded by the parabola: y = 4 – x2 and the X-axis.


Find the area of the region included between: y2 = 4x, and y = x


Find the area of the region included between: y2 = 4ax and the line y = x


Find the area of the region included between y = x2 + 3 and the line y = x + 3.


Choose the correct option from the given alternatives :

The area bounded by the regional 1 ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by ______.


The area enclosed between the parabola y2 = 4x and line y = 2x is ______.


The area of the region bounded by y = cos x, Y-axis and the lines x = 0, x = 2π is ______.


Choose the correct option from the given alternatives :

The area bounded by the parabola y2 = 8x, the X-axis and the latus rectum is


Choose the correct option from the given alternatives :

The area of the circle x2 + y2 = 25 in first quadrant is 


Choose the correct option from the given alternatives :

The area of the region bounded by the ellipse `x^2/a^2 + y^2/b^2` = 1 is


Choose the correct option from the given alternatives : 

The area bounded by the parabola y2 = x and the line 2y = x is


Choose the correct option from the given alternatives :

The area bounded by the ellipse `x^2/a^2  y^2/b^2` = 1 and the line `x/a + y/b` = 1 is


Choose the correct option from the given alternatives :

The area bounded by the parabola y = x2 and the line y = x is


Choose the correct option from the given alternatives :

The area of the region included between the line x + y = 1 and the circle x2 + y2 = 1 is


Solve the following :

Find the area of the region in first quadrant bounded by the circle x2 + y2 = 4 and the X-axis and the line x = `ysqrt(3)`.


Solve the following :

Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π


Solve the following :

Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = `pi/(3)`


Solve the following:

Find the area of the region lying between the parabolas: 4y2 = 9x and 3x2 = 16y


Solve the following :

Find the area of the region lying between the parabolas : y2 = x and x2 = y.


Solve the following:

Find the area enclosed between the circle x2 + y2 = 1 and the line x + y = 1, lying in the first quadrant.


Solve the following :

Find the area of the region bounded by the curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).


Solve the following :

Find the area of the region bounded by the straight line 2y = 5x + 7, X-axis and x = 2, x = 5.


The area bounded by the curve y2 = x2, and the line x = 8 is ______


The area enclosed by the line 2x + 3y = 6 along X-axis and the lines x = 0, x = 3 is ______ sq.units


Find the area bounded by the curve y = sin x, the lines x = 0 and x = `pi/2`


Find the area of the region bounded by the parabola y2 = 32x and its Latus rectum in first quadrant


Find the area of the region bounded by the curve y = x2, the X−axis and the given lines x = 0, x = 3


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


Find the area of the region bounded by the curves x2 = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant


Find the area of the region bounded by the curve y = sin x, the X−axis and the given lines x = − π, x = π


Find the area of the sector bounded by the circle x2+ y2 = 16, and the line y = x in the first quadrant


Find the area of the region bounded by the curve (y − 1)2 = 4(x + 1) and the line y = (x − 1)


The area bounded by the curve y = x3, the X-axis and the Lines x = –2 and x = 1 is ______.


Find the area common to the parabola y2 = x – 3 and the line x = 5.


Find the area bounded by the lines y = 5x – 10, X-axis and x = 5.


Find the area of the region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×