(a) Find the exact area of the surface obtained by rotating the curve y = e^x about the x-axis over the interval 0 ≤ x ≤ 1. (b) Determine the length of the parametric curve given by the following set of parametric equations. x = 3 cos t − cos 3t, y = 3 sin t − sin 3t, 0 ≤ t ≤ π You may assume that the curve traces out exactly once for the given range of t.
Vector Arithmetic
Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
(a) Find the exact area of the surface obtained by rotating the curve y = e^x about the
x-axis over the interval 0 ≤ x ≤ 1.
(b) Determine the length of the parametric curve given by the following set of
parametric equations.
x = 3 cos t − cos 3t, y = 3 sin t − sin 3t, 0 ≤ t ≤ π
You may assume that the curve traces out exactly once for the given range of t.
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