What is the x-coordinate of the center of mass - sets of

Question

Question 1.

(a) For the region bounded by the curve y = 1/25 xe^-5x and the positive x-axis, what is the total mass if the density is S per unit area?

(b) What is the x-coordinate of the center of mass?

Question 2.

How do the curves represented by the following two sets of parametric equations differ from each other in terms of extent and dynamics Illustrate with sketches. In both cases - ∞ < t < ∞

x = e^t/2        x = 3sin(t)

y = 4 - e^t     y = -5 + 9 cos²(t)

(a) Justify the claim that the graph of r = sinθ + cosθ is that of a circle.