Let y=p(x) be the parabola passing through the points (−1,0), (0,1) and (1,0). If the area of the region {(x,y):(x+1)2+(y−1)2≤p(x)} is A, then 12(π−4A) is equal to _____:
Explanation
Let the equation of parabola is
which pass through (1,0)
so
or
and {(x,y):(x+1)2+(y−1)2≤1,y≤p(x)}
⟹(x+1)2+(y−1)2≤1 represents interior part of the circle.
So required area is
A=∫−10(1−x2)dx−[1×1−4π×12]
Ab isse final value nikalte hain:
Explanation
Let the equation of parabola is
which pass through (1,0)
so
or
and {(x,y):(x+1)2+(y−1)2≤1,y≤p(x)}
⟹(x+1)2+(y−1)2≤1 represents interior part of the circle.
So required area is
A=∫−10(1−x2)dx−[1×1−4π×12]
Ab isse final value nikalte hain:
