Integration Problem

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natHenderson

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May 17, 2020
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I've tried to integrate f'(x) by hand but I couldn't do it, I even put it through some integral calculators, but they didn't give me an answer.
 
If you don't show us your work then it is not easy to help you solve your problem.
 
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This is what I've done so far, I feel like I shouldn't have used u-substitution, but I don't know what else to do.
 
The substitution isn't going to work anyway, but your first problem is on the fourth line. You need to put [math]\dfrac{1}{6x^2} ~ du[/math] in terms of u, you can't leave it in terms of x.

The second problem is when you integrated... You can't just pull the [math]\dfrac{1}{6x^2}[/math] out of the integral.

I wish I could help more but I can't think of a way to do it, either.

-Dan
 

natHenderson said:
View attachment 19186
I've tried to integrate f'(x) by hand but I couldn't do it, I even put it through some integral calculators, but they didn't give me an answer.
Click to expand...



See that instruction in capital letters?

This is using a TI-83 Plus:

If you put (*) into "Y =" **, and use "CALCULATE" 7: Integral
f(x)dx, lower limit 2 (ENTER) and upper limit 5 (ENTER), then
it will graph, shade under the curve, and give the
approximate area as 28.605496. ***

(*) the derivative function

** You might set the window as
Xmin = 2
Xmax= 5
Ymin = 0
Ymax = 15

Now, what about that f(2) = 0.4?

Are you going to 1) ignore it, 2) subtract it from ***, or
3) add it to *** to get one of the first three answers?
 
I'm going to add it which will give me 29.005 or A), thanks for your help, I just couldn't find a good online graphing calculator at the time and I didn't think the question needed it.
 
natHenderson said:
I'm going to add it which will give me 29.005 or A), thanks for your help, I just couldn't find a good online graphing calculator at the time and I didn't think the question needed it.
Click to expand...

I would ask some other users and helpers to check your conclusion.
I don't know for sure.
 
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