Question

The volume of revolution generated by rotating the function y = sin(2x)sqrt(cos(2x)) about the x-axis on the intevral [0, b] is pi/6 units^3, where 0 13 years ago

Answer 1

ok, what do we have here

Answer 2

they gave us the volume, we need to find the upper limit somehow!

Answer 3

the concept is simple enough ....

F(b) - F(a) = given volume soo

F(b) = given + F(a) and invert F(b)

Answer 4

right...? i'll take your word for it

Answer 5

youre a trusting soul lol

Answer 6

our function IS our radius, so go ahead and square it out

Answer 7

(sin(2x))^2*cos(2x)

Answer 8

good, and if youve done enough of these, that should look rather familiar

Answer 9

cos is the deriative of sin; so all we are missing is a 2 from that 2x

Answer 10

and maybe a 3 from the derivative of ^3

Answer 11

clean it up if you want with a usub;

u = sin(2x)

du = 2 cos(2x) dx

du/2 = cos(2x) dx

Answer 12

\[pi\int\frac{u^2 \ du}{2}\]

Answer 13

ahh i see. but then how do we find the upper limit?

Answer 14

well\[\int_{a}^{b} f(x)\ dx = F(b)-F(a)=given\ value\]

Answer 15

solve for b

Answer 16

pi [sin(2x)]^3
----------- ; at 0 this is 0 so that simply leaves us with
6


pi sin^3(2b)/6 = pi/6

Answer 17

when we compare it all up we are left with

sin^3(2b) = 1

Answer 18

since sin(pi/2) = 1

2b = pi/2

b = pi/4

Answer 19

you are amazing

Answer 20

nah, just lucky; i forgot the ^3 but that just hits the 1 and becomes pointless

Answer 21

so the answer is 0.79?

Answer 22

the answer is pi/4 if you have to approx it; then by all means ... approx away

Answer 23

yeah, says to the nearest hundredth.. thanks so much

Answer 24

your welcome

Answer 25

but you see how the concept panned out right?

Answer 26

yeah, i never thought of it like that

Answer 27

we left b alone till the end of it and it worked out for us :)

Answer 28

are you a teacher?

Answer 29

not that im aware of :)

Answer 30

haha, well nonetheless, you rock!