ine the slope of the tangent line at the non-pole point on C2 which inter he integral that gives the area of the region inside both C2 and C3.
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- Consider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface area of the solid obtained by rotating the region about the x-axis.Find the area enclosed by one loop of this polar curve: r=3sqrt(cos2theta) from 0 to 2pi using the formula A=1/2 integral from 0 to 2pi (r)^2 for parametric curve.Find the area of the surface of revolution generated by revolving the curver = 2acos(theta) about the initial line.
- Use the integration capabilities of a graphing utility to approximate the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 4 cos 2θ, [0, π/ 4]Use a polar double integral to find the area enclosed by the threepetaled rose r = sin 3θ.Given two polar curves and r=2cos2θ , r =1 as in Figure 1. Find the area of the shaded region by using the single integration in polar coordinates.