Let S be the solid obtained by rotating the region shown in the figure about the
ID: 2845005 • Letter: L
Question
Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a=6 and b=2) be sure to answer all parts.
Sketch a typical approximating shell.
What are its circumference c and height h?
c(x) =
h(x) =
Use shells to find the volume V of S.
V =
Let S be the solid obtained by rotating the region shown in the figure about the y - axis. (Assume a = 6 and b = 2) be sure to answer all parts. Sketch a typical approximating shell. What are its circumference c and height h? Use shells to find the volume V of S.
Explanation / Answer
Circumference is 2pi x.
Height is 6x (x-2)^2
integral is 2pi int x * 6x (x-2) dx from x=0 to x=2
2pi int (6x^4 -24x^3 +24x^2) dx
Antiderivative is 6/5 x^5 - 6x^4 +8x^3
Evaluate from 0 to 2 and we have 2pi *32/5 = 64pi/5.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.