Question
Find the area of the region bounded by the curve r=sinθ+cosθand lies in the sector 0≤θ≤π
Answers
Lilac
Did you figure out the answer?
oobleck
a = ∫[0,π] 1/2 (sinθ+cosθ)^2 dθ = (3π+2)/8 = 1.481
This seems reasonable, since the curve is the circle
(x - 1/2)^2 + (y - 1/2)^2 = 1/2
which has area π/2, but we have excluded a small segment subtending an arc of θ=π/2, with an area of 1/4 (π/2 - 1)
This seems reasonable, since the curve is the circle
(x - 1/2)^2 + (y - 1/2)^2 = 1/2
which has area π/2, but we have excluded a small segment subtending an arc of θ=π/2, with an area of 1/4 (π/2 - 1)
oobleck
my bad. The area is ∫[0,3π/4]