# 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