Question

For Velocity and Net change... Anyone understand?

Answer 1

@zachdykstra plz tell the question:)

Answer 2

Find the displacement over the given interval

v(t) = t^3 - 5t^2 + 6t

with the given area of

[0 \le t \le 2pie]

Answer 3

displacement is the integration of velocity

Answer 4

explain in simpler terms??

Answer 5

the thing that you are looking to find is the area under the function from 0 to 2pi

Answer 6

... antiderivative perhaps?

Answer 7

velocity is simply the rate at which distance changes with time so displacement is integration of velocity equation and integeration simply means area under curve :)

Answer 8

so do you guys usually just use desmos or CAD calculators to calculate it?

Answer 9

pencil and paper .. no eraser

Answer 10

\[\int x^n=\frac 1{n+1} x^{n+1}\]

Answer 11

yeah I understand quite simply the antiderivative and substitution and all of the equations but the graphing and finding the area of is what is kicking my butt

Answer 12

theres no need to graph it if you understand how to take an antiderivative/ integral

Answer 13

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

Answer 14

so if it tells me to find the displacement of

t^3 - 5t^2 + 6t

with the given interval [0 less than or equal to T which is less than or equal to 2pi]

Answer 15

@amistre64 good going :)

Answer 16

a = 0, b = 2pi, f(x) = f(t) = t^3 - 5t^2 + 6t

\[\int_{0}^{2\pi}~t^3 - 5t^2 + 6t~dt\]
you do know how to integrate a power right?

Answer 17

thnx :)

Answer 18

yeah i understand all of that you just wrote im just lost after that in finding the answer

Answer 19

ok, what do we get for the integration? lets see if you have that done correctly then

Answer 20

so I take the anti-derivative or derivative from that?

Answer 21

yes

Answer 22

take the "antiderivative" that is

Answer 23

okay so it becomes n+1/n+1 or whatever but i have no idea how to type that all special

Answer 24

just type it in the best you can, im smart enough to be able to see what it is you might be trying to accomplish :)

the antiderivative of: \(t^3 - 5t^2 + 6t\) is?

Answer 25

t^4/4 - 5t^3/3 + 3t^2

Answer 26

perfect..

now to find out the rest, we need to subtract that from itself

(t^4/4 - 5t^3/3 + 3t^2) - (t^4/4 - 5t^3/3 + 3t^2)

and evaluate it at t = 2pi on the left, and t=0 on the right

((2pi)^4/4 - 5(2pi)^3/3 + 3(2pi)^2) - (0^4/4 - 5(0)^3/3 + 3(0)^2)

16pi^4/4 - 40pi^3/3 + 6pi^2 - 0

Answer 27

simplify as desired