Area Of Region In First Quadrant Enclosed By X Axis Line Y X And Circle X2 Y2 32 Is

Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 … units (c) 32π sq. units …

Answers:

(b) We have, y = 0, y = x and the circle x² + y² = 3 in the first quadrant  .

Solving y = x with the circle 
x² + x² = 32
⇒ x² = 16
⇒ x = 4
When x = 4, y = 4
For point of intersection of circle with the x-axis,
Put y = 0
∴ x² + 0 = 32
⇒ x = ± 4√2
So, the circle intersects the x-axis at (± 4√2,0)
From the figure, area of shaded region