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math456

  • 2 years ago

Can anyone help me with solving this integral?

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  1. math456
    • 2 years ago
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    \[\int\limits_{2}^{5} (4-2x)dx\]

  2. amistre64
    • 2 years ago
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    which part is giving you night terrors?

  3. math456
    • 2 years ago
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    lol the 2nd one!

  4. amistre64
    • 2 years ago
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    what is the integration rule for x^n ?

  5. math456
    • 2 years ago
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    \[\int\limits_{2}^{5} 4.dx - 2\int\limits_{2}^{5}x.dx\]

  6. amistre64
    • 2 years ago
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    or you can think of it in terms of derivatives; what is the derivative rule for x^n ?

  7. math456
    • 2 years ago
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    nx^n-1

  8. amistre64
    • 2 years ago
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    good, now how would you undo that? which is all an integration is ... undoing a derivative

  9. math456
    • 2 years ago
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    thats wht i am having trouble with!

  10. amistre64
    • 2 years ago
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    divide by n and add 1 back to the exponent

  11. amistre64
    • 2 years ago
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    \[x=x^1\]right?

  12. math456
    • 2 years ago
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    x^1

  13. math456
    • 2 years ago
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    yea

  14. amistre64
    • 2 years ago
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    \[x^1=x^{2-1}\]so n=2 in this case

  15. math456
    • 2 years ago
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    ohh yea right!

  16. amistre64
    • 2 years ago
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    so, does x^2 derive down to 2x?

  17. math456
    • 2 years ago
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    yea it will be 2x^2-1

  18. math456
    • 2 years ago
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    but we need x!

  19. amistre64
    • 2 years ago
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    but we already have a 2x

  20. amistre64
    • 2 years ago
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    you dont HAVE to pull out the constant. In this case it acutally helps out

  21. math456
    • 2 years ago
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    2x/2

  22. amistre64
    • 2 years ago
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    \[\frac d{dx}x^2=2x\] \[\int 2x~dx=x^2\]

  23. math456
    • 2 years ago
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    ohh gotch yea so, its gona be like (5-2)^2

  24. amistre64
    • 2 years ago
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    \[\int\limits_{2}^{5} 4.dx - \int\limits_{2}^{5}2x.dx\] \[4x(5,2) - x^2(5,2)\] \[[4(5)-4(2)] - [(5)^2-(2)^2]\]

  25. math456
    • 2 years ago
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    so i was doing just 1 term of x

  26. amistre64
    • 2 years ago
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    you were mixing up the subtraction and the function into an ungodly abomination :)

  27. math456
    • 2 years ago
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    yea right, i got it now! Thank you very much.. :)

  28. amistre64
    • 2 years ago
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    \[\int_{a}^{b} f(x)~dx=F(b)-F(a)~NOT~F(b-a)\]

  29. math456
    • 2 years ago
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    -9

  30. amistre64
    • 2 years ago
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    20-8-(25-4) 20-8-25+4 24 - 33 = -9 yes

  31. math456
    • 2 years ago
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    yayy.. thanks again!

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