## AmTran_Bus one year ago Integration help

1. AmTran_Bus

|dw:1440354731938:dw|

2. AmTran_Bus

The integral of x is just (x^2)/2, right?

3. freckles

yea

4. freckles

well +c but we don't care about +c really with definite integrals

5. AmTran_Bus

So I have|dw:1440354893717:dw|

6. AmTran_Bus

or b^2/2 - a^2/2 (1/b-a)?

7. ganeshie8

right, but nobody leaves it like that.. it can be simplified...

8. AmTran_Bus

|dw:1440355025079:dw| can you help with the bottom?

9. freckles

$\frac{1}{2} \frac{b^2-a^2}{b-a}$ hint difference of squares

10. AmTran_Bus

Oh ok. Not too bad then. Can more be done? The book says b+a / 2

11. freckles

(b+a)/2 is correct

12. freckles

and you can't do anything else unless you want to write it as b/2+a/2

13. AmTran_Bus

can you show me how you get from 1/2 (b^2-a^2 / 2(b-a) to that?

14. freckles

do you know the difference of squares formula...

15. freckles

that was my hint

16. freckles

so maybe not.. b^2-a^2=(b-a)(b+a)

17. AmTran_Bus

Ok thanks that was the missing piece for me I guess.

18. freckles

hmmm how did you get that extra 2 ?

19. freckles

$\frac{1}{b-a} \int\limits_a^b x dx \\ \frac{1}{b-a} \cdot \frac{x^2}{2}|_a^b \\ \frac{1}{b-a}(\frac{b^2}{2}-\frac{a^2}{2} ) \\ \frac{1}{b-a} (\frac{b^2-a^2}{2}) \\ \frac{1}{2} \frac{b^2-a^2}{b-a} \\ \frac{1}{2} \frac{(b-a)(b+a)}{b-a}$ you should just have one 2 on bottom not two 2's

20. freckles

"can you show me how you get from 1/2 (b^2-a^2 / 2(b-a) to that?" or was the extra 2 just a type-o?

21. AmTran_Bus

Oh me! Yes, I accidentally put in an extra 2 on the bottom, forgetting the 1/2!

22. freckles

oh okay