मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

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

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

Let A be the required area.

Given equation of the curve is 4y = 7x + 9

i.e., y = `(7x + 9)/4`

∴ A = `int_2^8 y  "d"x`

= `int_2^8 (7x + 9)/4  "d"x`

= `1/4 int_2^8 (7x + 9)  "d"x`

= `1/4[7(x^2/2) + 9x]_2^8`

= `1/4[[7(8^2/2) + 9(8) - 7(2^2/2) + 9(2)]]`

= `1/4[224 + 72 - (14 + 18)]`

= `1/4(296 - 32)`

= `1/4(264)`

∴ A = 66 sq.units

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.7: Application of Definite Integration - Q.2

संबंधित प्रश्‍न

Using integration find the area of the region {(x, y) : x2+y2 2ax, y2 ax, x, y  0}.


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 of the region bounded by the parabola y = x2 and y = |x| .


Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.


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


Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12


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} .


Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9  "at" (-1,2sqrt2)`.


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:

y = x2 + 1, x = 0, x = 3


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 _______.


Area of the region bounded by x2 = 16y, y = 1 and 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 _______.


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 circle x2 + y2 = 16 is ______


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 = 4y, the Y-axis lying in the first quadrant and the lines y = 3


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


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


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


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


Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.


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


The area bounded by the curve | x | + y = 1 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×