Calculus Theorem Question

1. Mar 22, 2016

1. The problem statement, all variables and given/known data

Can any body give me hint how to find K if F(x)= 3x+2

The integral lower part is not the same, , how to deal with his?

2. Relevant equations

3. The attempt at a solution

Please ,I need hint to start

Last edited by a moderator: Mar 22, 2016
2. Mar 22, 2016

Staff: Mentor

3. Mar 22, 2016

PeroK

... or, why not just integrate what you've been given?

4. Mar 22, 2016

Ray Vickson

What is preventing you from just computing $\int_2^x (3t + 2) \, dt$ and $\int_8^x (3t + 2) \, dt$?

5. Mar 29, 2016

Thank you all,

The point guys is that , first integration is start from 2 and the other one is start from 8.
Hence if I have only the base 2, the answer will be 3x+2 =3x+2(but the problem is the second base is 8), cant figure out what I missing till now???

How can I equate them?

Thanks again

6. Mar 30, 2016

Staff: Mentor

That's not a valid answer for that definite integral.

Last edited: Mar 30, 2016
7. Mar 30, 2016

Thanks

Could you upload refer to examples with X is the boundary of indefinite integral not numbers?

8. Mar 30, 2016

Samy_A

When a math problem proves to be too difficult, it is a good idea to work on it in little pieces.

Why don't you do as has been suggested above: forget about the exercise itself, and just compute the following integral:
$\int_2^x (3t + 2) dt$.

What result do you get?

9. Mar 30, 2016

HallsofIvy

Staff Emeritus
What, exactly, is your difficulty? Have you been able to find an anti-derivative for 3t+ 2? That is, can you find $\int 3t+ 2 dt$? What do you get when you substitute the upper and lower bounds and subtract?

10. Mar 30, 2016

11. Mar 30, 2016

Samy_A

No.
Let's go one more step back (as suggested by HallsofIvy): what is the indefinite integral $\int (3t +2) dt$?

12. Mar 30, 2016

Ssnow

Sorry, a stupid question but $F(x)=3x+2$ is a primitive of $f$ or it is the $f$ in the integral?

13. Mar 30, 2016

Samy_A

That's not a stupid question, it's a good catch.

14. Mar 30, 2016

Ssnow

Ah ok because in one case one must apply directly the Fundamental calculus theorem and in the other side one must find before the primitive ... @keewansadeq you must reflect on this ....

15. Mar 30, 2016

Staff: Mentor

I noticed that as well. It could be that F is an antiderivative of f, or, as often happens, some posters mix upper and lower case for a single variable name.
@keewansadeq, did you intend f and F to represent different functions?

16. Mar 30, 2016

HallsofIvy

Staff Emeritus
I assumed it was the integrand because there would not be a specific constant, like 2, in the anti-derivative. If the itegrand is f(x)= 3x+ 2, then the integrand is $F(x)= (3/2)x^2+ 2x+ C$ where C is a constant that will cancel in the definite integral. If the integrand is the constant, 3, then the anti-derivative is 3x+ C, to be evaluated at 2 and x on one side, 8 and x on the other.

17. Mar 30, 2016

Ssnow

@HallsofIvy I have had the same doubt the fact is that it is possible that in the text of the schedule they choose a particular primitive of $3$ with $c=2$, I don't know because usually with $F$ denotes the primitive ...

18. Mar 31, 2016

Yes I did, Capital F means anti antiderivative

19. Mar 31, 2016

Actually,I am very goof in integration,but I am week in Fundamental calculus theorem, it is to me that derivative of integration will be the same function, that why I am confused.

Thanks all I appreciate

20. Mar 31, 2016

This is simple

3(t^2)/2+2t

But the main problem is with Fundamental calculus theorem