Question

Find the area of sector bounded by the circle x² + y² = 25, in the first quadrant−

Answer 1

Given equation of the circle is x² + y² = 25

∴ y² = 25 − x²

∴ y = `+-  sqrt(25 - x^2)`

∴ y = `sqrt(25 - x^2)`    .....[∵ In first quadrant, y > 0]

∴ Required area = `int_0^5 y  "d"x`

= `int_0^5 sqrt(25 - x^2)  "d"x`

= `[x/2 sqrt(25 - x^2) + 25/2 sin^-1 (x/5)]_0^5`

= `0 + 25/2 sin^-1 (1) - 0`

= `25/2 (pi/2)`

= `(25pi)/4` sq.units