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The area of the region \(x, y): y2 4x, x<4, xy(x-1)(x-2)(x-3)(x-4)>0, x 3 \ is
(1) 323
Sign of y must equal the sign of h(x)= x(x-1)(x-2)(x-3)(x-4), 0<x<4
h>0 on (0,1) (2,3) ⇒ upper half (y>0); h<0 on (1,2) (3,4) ⇒ lower half (y<0)
[figure]
∵ the parabola is symmetric about the x-axis, each shaded strip = area of one half over that interval
Area = 04 2 x dx= 43 [x3/2 ]04= 323
Answer: (1)
The area of the region enclosed by the parabolas y=4x-x2 and 3y=(x-4)2 is equal to :
The area (in square units) of the region bounded by the parabola y2=4(x-2) and the line y=2x-8, is :
The area of the region enclosed by the parabola (y-2)2=x-1, the line x-2 y+4=0 and the positive coordinate axes is .
The area (in sq. units) of the part of the circle x2+y2=169 which is below the line 5x-y=13 is 2 - 652+ -1 ( 1213 ), where , are coprime numbers. Then + is equal to .
Let the area of the region \(x, y): 0 x 3, 0 y \x2+2, 2x+2 \ \ be A. Then 12 A is equal to .
Let the area of the region \(x, y): x-2y+4 0, x+2y2 0, x+4y2 8, y 0 \ be mn, where m and n are coprime numbers. Then m+n is equal to .
If the area of the region \(x,y):0 y \2x,6x-x2 \ \ is A, then 12A is equal to .