Calculus & Analytic Geometry (B.A / B.Sc.)
Chapter:06 (Plane Curve II)
In this chapter, we will study the following topics:
- length of arcs
- arc-length in cartesian coordinates
- length of loop of the curve
- arc-length in the parametric form of the equation of the curve
- length of the cycloid
- arc-length in polar coordinates
- polar equation
- length of the cardioid
- length of the catenary
- the entire length of the astroid
- intrinsic equations
- derivation of the intrinsic equation from the cartesian equation
- derivation of the intrinsic equation from the polar equation
- the intrinsic equation of the cycloid
- the intrinsic equation of the equiangular spiral
- curvature
- angles of contingency
- radius of curvature
- curvature and radius of curvature in cartesian coordinates
- the radius of the curvature of the logarithmic spiral
- coordinates of the center of the curvature
- involutes and evolutes
- the evolute of the curve
- properties of the evolute
- a rule of drawing the involute
- computing areas in rectangular coordinates
- areas between two curves
- computing areas in polar coordinates
- proper limits of integration
- points of intersection
- find the area between the values of the curve
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