# Math Help - Integral Help Please :D

1. ## Integral Help Please :D

Hey everyone, hope someone can help me with this problem. I just got back from Spring Break and for some reason have forgotten how to do this... Thanks in advance for any help you can give me!

Suppose that in a memory experiment the rate of memorizing is given by:
M'(t)=-0.009t^2+0.2t
where M'(t) is the memory rate in words per minute. How many words are memorized in the first 10 minutes (from t=0 to t=10) ?

2. Originally Posted by FGCUguy
Suppose that in a memory experiment the rate of memorizing is given by:
M'(t)=-0.009t^2+0.2t
where M'(t) is the memory rate in words per minute. How many words are memorized in the first 10 minutes (from t=0 to t=10) ?
integrate words per minute over a period of minutes ...

number of words = $\int_0^{10} M'(t) dt$

3. Originally Posted by skeeter
integrate words per minute over a period of minutes ...

number of words = $\int_0^{10} M'(t) dt$
Thank you for the help, but as dumb as it may sound, I just have no clue where to start. I feel like I don't get taught any of this stuff. Do you have any links or anything that would explain how to integrate the function?

4. Suppose that in a memory experiment the rate of memorizing is given by:
M'(t)=-0.009t^2+0.2t
where M'(t) is the memory rate in words per minute. How many words are memorized in the first 10 minutes (from t=0 to t=10) ?

int(int(-.009t^2 + .2t))

integrate:

int(.003t^3 + .1t^2 + c)

integrate again:

.00075t^4 + .03333...t^3 +cx +d)

plug in 10:

7.5 + 33.333... +10c +d

245/6 + 10c +d

5. Originally Posted by skeeter
integrate words per minute over a period of minutes ...

number of words = $\int_0^{10} M'(t) dt$
wait actually i think i sort of remember something, do I find the antiderivative of something and divide it by the other?

6. $\int_0^{10} -0.009t^2+0.2t \, dt$

$\left[-.003t^3 + 0.1t^2\right]_0^{10}$

$[-.003(10^3) + 0.1(10^2)] - [0 + 0]$

$-3 + 10 = 7$ words

7. wow that helped a ton. Thank you so much. If I'm understanding this correctly, I find the antiderivative and substitute 10 for t, then do the same and substitute 0 for t, and subtract the first (the one i substituted 10) and subtract the second (the one i substituted 0)? If that made any sense haha.

8. Originally Posted by FGCUguy
wow that helped a ton. Thank you so much. If I'm understanding this correctly, I find the antiderivative and substitute 10 for t, then do the same and substitute 0 for t, and subtract the first (the one i substituted 10) and subtract the second (the one i substituted 0)? If that made any sense haha.
You find the antiderivative and substract highest from lowest, in this case (t=10) - (t=0) indeed.

9. Originally Posted by FGCUguy
wow that helped a ton. Thank you so much. If I'm understanding this correctly, I find the antiderivative and substitute 10 for t, then do the same and substitute 0 for t, and subtract the first (the one i substituted 10) and subtract the second (the one i substituted 0)? If that made any sense haha.