Find the length of the curve given by the following parametrization:𝑥 = 8 cos 𝑡 + 8𝑡 sin 𝑡 , 𝑦 = 8 sin 𝑡 − 8𝑡 cos 𝑡 , 0 ≤ 𝑡 ≤

r = 8 + 8 cos(𝜃)r = 8 − 8 sin(𝜃)r ≥ 0, 0 ≤ 𝜃 < 2𝜋

Both the red and blue line segments stretch from the center of the circle to a point on the circle. The length of the blue line segment is 8. How long is the red line segment?

Find the length of the curve over the given interval.polar equationr = 10a cos(𝜃)interval

Find the length of the curve C which is parametrized by r(t) = (2 cos t, 2 sin t, √5 t) for0 ≤ t ≤ 2

Sketch the region enclosed by the given curves.y = 4 cos(𝜋x),    y = 8x2 − 2 Find its area.