Question

work integral problem

Answer 1

A tank was designed by revolving the parabola y=4x^2, 0lessthanorequaltoXlessthanorequalto2, about the x-axis. The tank, with dimensions in meters, is filled with water weighing 9800 N/m^3. How much work will it take to empty the tank by pumping water to the top of the tank? give answer in nearest J.
Answers are:
15,762,255
5,254,418
164,201
1,313,605
Please help me understand this with all the steps.

Answer 2

\[0\le x \le2\]

Answer 3

why did you take it off?

Answer 4

it had a slight error, one sec

Answer 5

oh, ok.

Answer 6

k i have to go in like 10 minutes, so can you please put down what you can?

Answer 7

ok sure, not sure if this answer's right but maybe it helps
work=f.d=weight*height=integrate(weight(y)*(16-y) dy)=integrate(9800*area(y)*(16-y) dy) from y=0 to y=16
area(y)=pi*x^2=pi*y/4
leaving 9800*pi*integrate(y/4*(16-y) dy) from y=0 to y=16
5.254*10^6

Answer 8

so where di the 16 come from?

Answer 9

16 is the maximum height/y-value, 16-y is the distance that water located at height y needs to travel to reach the top of the tank

Answer 10

(y=16 at x=2)

Answer 11

oh ok. i'll read through and try to figureit out realquick

Answer 12

Now, that makes sense. I now understand what it all means. Thank you! now i can identify which parts are which. you are awesome!

Answer 13

glad that helped :)