Volume help:

Question

Volume help:

luigi0210 · Answer

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

lncognlto · Answer

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

lncognlto · Answer

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

luigi0210 · Answer

Why is it those?

agent0smith · Answer

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 $$\large \sin^2 x= \frac{ 1- \cos 2x }{ 2}$$

luigi0210 · Answer

Oh I see, thank you!

luigi0210 · Answer

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

luigi0210 · Answer

Thanks @lncognlto and @agent0smith :)

lncognlto · Answer

1/2 x pi^2 is correct :)