Asked by LilPeep
Find the area of the region bounded by the curves y = sin^-1(x/6), y = 0, and x = 6 obtained by integrating with respect to y. Please include the definite integral and anti-derivative.
Answers
Answered by
Steve
y = sin^-1(x/6)
x = 6 siny
The boundaries define one-half of an arch on the curve, so the area is
∫[0,π/2] 6siny dy = 6
x = 6 siny
The boundaries define one-half of an arch on the curve, so the area is
∫[0,π/2] 6siny dy = 6