Problem 34 Hard Difficulty
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.
$ y =x^2 $ , $ x^2 + y^2 = 1 $ , $ y \ge 0 $
(a) About the x-axis
(b) About the y-axis
Answer
a) $V=\pi \int_{-0.786}^{0.786} 1-x^{2}-x^{4} d x \approx 3.544596$
b) $V \approx 1$
Topics
Applications of Integration
Discussion
Top Calculus 2 / BC Educators
Heather Z.
Oregon State University
Kayleah T.
Harvey Mudd College
Caleb E.
Baylor University
Samuel H.
University of Nottingham
Watch More Solved Questions in Chapter 6
Video Transcript
the problem is said happened to grow for the volume off the solid between the band rotating the region. Vanzi, the bad acumen curves are party to specify the line. Then use your calculator to you. Moderated Integral racked into five decimal places. But a about ex Alexis I'd be out waxes the first we can stanched a graph off this region. So the region is this part. First the went into computers and coordinate intersection points of this to curves. So we have Why couldn't you explain? Exclaimed Plus y squared equals one supplying Why would square here? This is why plus y squared you could What? So why this record too negative Half a glass return our over Jew So you think your printer make tio half us until five over two Here I didn't notice this number I pay on December I b now for part of a about max access Oh, how this's negative, b, you know, And for each acts the cross section is a washer in your riders Yes, he called to X squared after writers is the cultural long Linus, explain this one Yes, Over half the volume Wait is this culture Hi arms integral around negative b to be Hi negative one month's explain Squire Month That's two four max thiss iss in culture three point off warm for nine. A party about the y axis. The first we can see this part is it's my trick about waxes Andi. I went wide it. It's written by two parts. This's Hey, why could tow eh? So above why I could tow eh? So it's a cross section is uh please the riders is cultural one minus y squared. Your shift is one below wind could eh? The class section is peace. The wind years is he called you good stuff. Why then? The volume V is a cultural integral from zero to a Hi. Why squire you want? Plus, it's girl from paint one high. You have one minus life square the way you want. Author is year old point nine nine nine nine eight
Topics
Applications of Integration
Top Calculus 2 / BC Educators
Heather Z.
Oregon State University
Kayleah T.
Harvey Mudd College
Caleb E.
Baylor University
Samuel H.
University of Nottingham
