Question

Volume help:

Answer 1

If a football is formed by rotating the sine curve y=sinx from zero to pi about the x axis, find the volume of the football

Answer 2

\[v = \int\limits_{0}^{\pi} y ^{2} dx\]

Answer 3

\[v = \int\limits_{0}^{\pi} \sin ^{2}x dx\]

Answer 4

Why is it those?

Answer 5

Use the disk method for around the x axis
\[\Large V = \pi \int\limits_{a}^{b} R^2 dx\]where R is the radius, dx is the thickness of the disk, in this case your limits are 0 to pi, radius of the disk is sinx:

\[\Large V = \pi \int\limits\limits_{0}^{\pi} (\sin x)^2 dx\]
Easiest way to integrate sin^2 x is to use the trig identity \[\large \sin^2 x= \frac{ 1- \cos 2x }{ 2}\]

Answer 6

Oh I see, thank you!

Answer 7

Final answer being 1/2(pi)^2 right?

Answer 8

Thanks @lncognlto and @agent0smith :)

Answer 9

1/2 x pi^2 is correct :)