Question

Let f be a function defined on the closed interval [-3,9]. The graph of f, consists of three line segmants shown above. Let g(x) = integal from 0 to x f(t)dt. Find the average value of f on the closed interval [-3,5]. See attached for graph.

Answer 1

\[g(x) = \int\limits_{0}^{x}f(t)dt\]

graph

Answer 2

I know that average value is \[\frac{ 1 }{ 8 }\int\limits_{-3}^{5}f(t)dt\] but i keep getting the wrong answer. the answer's supposed to be 29/8.

Answer 3

@zepdrix can you help?

Answer 4

So we're not told what \(\large f(t)\) is?
Hmmm there must be a trick to this.
I can't quite see it D:

Grr yer graph is so tiny lol.

Answer 5

no. is it just the area from -3 to 5 ?
sorry. i can't make it much bigger. put it on word and stretch it out?

Answer 6

Ooooo much better c:

Answer 7

Oh I guess what you're suppose to do is ~ split it up into a couple of integrals.

\[\large \int\limits_{-3}^3 f(t)\;dt \qquad + \int\limits_3^5 f(t)\;dt\]

See how the function changes from one linear function to another at t=3?

Answer 8

crap...
sorry accidentally deleted

Answer 9

So we want to form equations for those lines.

Answer 10

I think.

Answer 11

sorry, why would you need the equations of those lines? can't u just use like the formulas for trapezoids and triangles to find the area under the lines?

Answer 12

Mmmmm yah that might be easier! :)

Answer 13

Ok lemme try that, and see if I come up with the same answer as you =o

Answer 14

k. lemme do it again

Answer 15

oh oh woops. I drew that poorly :) lemme fix that.

Answer 16

about that 6-6-3 trapezoid, would you have to break that up into two because one side of that thing is on the negative side?