Question

Using integration find the area of the region in the first quadrant enclosed by the x-axis, the line y = x, ad circle x2 + y2 = 32

Answer 1

x2 + y2 = 32 and centre (0,0)

∴ radius = r = √32 = 4√2

Equation are y = x ….(1) and x2 + y2 = 32 …..(2)

∴ x2 + x2 = 32 (using (1) and (2))

∴ 2x2 = 32 ⇒ x2 = 16 or x = ±

since region is in first quadrant

x = 4 ⇒ y = 4

∴ Required Area = Area OBM + Area MBA