Question

Help finding volume of solid

Answer 1

@satellite73

Answer 2

@zepdrix

Answer 3

draw

Answer 4

desmos?

Answer 5

you need to draw the thing first.

Answer 6

https://www.desmos.com/calculator/abc9opgrzj

Answer 7

okay, so now, do you want to use disk method or what?

Answer 8

yeah disk

Answer 9

\[
V = \int_{-\pi/2}^{3\pi/2}\pi r^2(x)\;dx
\]

Answer 10

What do you think \(r(x)\) would be in this case?

Answer 11

That's what was giving me trouble. Do I subtract the 4 sin(x)+2 and 6? I dont think that's right. How do I use double angel formulas with this problem?

Answer 12

uh, it's just \(6-4\sin(x)+2\)

Answer 13

you have to square it.

Answer 14

Right I understand that part. I was just confused because the program said to use the double angel trig formulas...

Answer 15

i think I got it from here, thanks

Answer 16

you will have to deal with a squared sin term.

Answer 17

which is dealt with using half angle, or even double angle.

Answer 18

\[\int\limits_{?}^{?}16 \sin^2 (x) dx= 8x-4\sin(2) ???\]

Answer 19

ive never used double angle before

Answer 20

\[
\sin^2(x) = \frac{1-\cos(2x)}{2}
\]

Answer 21

It's really the half angle formula in this case.

Answer 22

8(1-cos(2x))

Answer 23

@Hamoody1996

Answer 24

are you still stuck?

Answer 25

is it : pi(8(1-cos(2x)-64cos(x)+64x

Answer 26

Is that the integrand you are getting?

Answer 27

that's the indefinite integral

Answer 28

why do you have two \(\cos\) in there?

Answer 29

48pi^2 is the answer. I used 4sin(x)-4

Answer 30

as r(x)