Surface area of solid of revolution

/4 Comments/in /by

If we revolve a curve y=f(x)  on the interval [a,b] about x axis, then we calculate area of resulting surface by breaking the curve into pieces as we did for arc length. A piece of curve of length dS at an average  distance y from x axis traces out a surface that is well approximated by a slice of a cone whose area is approximated by 2πydS.

\dpi{120} \mathbf{S=\int_{a}^{b}2\pi (radius)(arc length)dx}

For detailed explanation and examples please visit… https://celestialtutors.com/subtopic/surface-area/

How to find Arc Length of different curves ?

/0 Comments/in /by

Length of a curve is called arc length.The method of finding arc length for different type of curves is very much similar, yet different formulas are used for them. Here we are going to study these formulas one by one.

To find arc length of a curve defined  by function f(x) over a certain interval [a,b] we use the following formula…

\dpi{120} \mathbf{L=\int_{a}^{b}\sqrt{1+[f'(x)]^{2}}dx}

Find more detailed work and examples here… https://celestialtutors.com/subtopic/arc-length/