Question

find the are of the region in the first quadrant enclosed by the x-axis,the line y=x,and the circle x2+y2=32.

Answer 1

8cm^2 is the required answer.

Answer 2

Answer:

4 π    sq unit

Step-by-step explanation:

x² + y² = 32

=> radius = √32 = 4√2 cm

Origin is cenetr

y = x  will  cut at

x² + x²  = 32

=> 2x² = 32

=> x² = 16

=> x =  ±4

in the first quadrant x = 4 ,  y = 4

Angle between x - axis and y = x

is Tan⁻¹(1/1)  = 45°

Area of egion in the first quadrant enclosed by the x-axis,the line y=x,and the circle x² + y² = 32

= (45/360) π R²

= (1/8) π 32

= 4 π   sq unit