math456 2 years ago Can anyone help me with solving this integral?

1. math456

$\int\limits_{2}^{5} (4-2x)dx$

2. amistre64

which part is giving you night terrors?

3. math456

lol the 2nd one!

4. amistre64

what is the integration rule for x^n ?

5. math456

$\int\limits_{2}^{5} 4.dx - 2\int\limits_{2}^{5}x.dx$

6. amistre64

or you can think of it in terms of derivatives; what is the derivative rule for x^n ?

7. math456

nx^n-1

8. amistre64

good, now how would you undo that? which is all an integration is ... undoing a derivative

9. math456

thats wht i am having trouble with!

10. amistre64

divide by n and add 1 back to the exponent

11. amistre64

$x=x^1$right?

12. math456

x^1

13. math456

yea

14. amistre64

$x^1=x^{2-1}$so n=2 in this case

15. math456

ohh yea right!

16. amistre64

so, does x^2 derive down to 2x?

17. math456

yea it will be 2x^2-1

18. math456

but we need x!

19. amistre64

but we already have a 2x

20. amistre64

you dont HAVE to pull out the constant. In this case it acutally helps out

21. math456

2x/2

22. amistre64

$\frac d{dx}x^2=2x$ $\int 2x~dx=x^2$

23. math456

ohh gotch yea so, its gona be like (5-2)^2

24. amistre64

$\int\limits_{2}^{5} 4.dx - \int\limits_{2}^{5}2x.dx$ $4x(5,2) - x^2(5,2)$ $[4(5)-4(2)] - [(5)^2-(2)^2]$

25. math456

so i was doing just 1 term of x

26. amistre64

you were mixing up the subtraction and the function into an ungodly abomination :)

27. math456

yea right, i got it now! Thank you very much.. :)

28. amistre64

$\int_{a}^{b} f(x)~dx=F(b)-F(a)~NOT~F(b-a)$

29. math456

-9

30. amistre64

20-8-(25-4) 20-8-25+4 24 - 33 = -9 yes

31. math456

yayy.. thanks again!