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anonymous

  • 5 years ago

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  1. anonymous
    • 5 years ago
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  2. anonymous
    • 5 years ago
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    okay so you can separate the integral like \[\int\limits_{-5}^{1}f(x) dx= \int\limits_{-5}^{0}82xdx+ \int\limits_{0}^{1}6x^2dx\]

  3. anonymous
    • 5 years ago
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    technically you would have to evaluate the lower limit of the integral of the second term ( the 0 in the 6x^2 integral ) at some letter (a,b,c ect what ever letter you like). then you take the limit of the letter as it approaches the zero that is there as you see it above.

  4. anonymous
    • 5 years ago
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    So in a more punctual approach the integral should be \[ \int\limits_{1}^{-5}f(x) dx = \int\limits_{-5}^{0}82x dx + \lim_{a \rightarrow 0} \int\limits_{a}^{1}6x^2dx\]

  5. anonymous
    • 5 years ago
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    It's kind of technicality you will definitely see in later calculus called improper integrals. The REASON for this is because of the inequality \[x > 0\] which means the x on that interval never actually reaches zero, so you say as x --> 0 (as x approaches zero, 0.00000001 and smaller). Now just take the integral of either one, the second one is the most correct if you understand the limit deal. but both will give you the same answer.

  6. anonymous
    • 5 years ago
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    then how do u do it with that limit?

  7. anonymous
    • 5 years ago
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    you would evaluate the integral first then take the limit. so \[\lim_{a \rightarrow 0} \int\limits_{a}^{1} 6x^2dx = \lim_{a \rightarrow 0} 6x^3/3- a \rightarrow1\]

  8. anonymous
    • 5 years ago
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    then \[6(1)^3/3 - \lim_{a \rightarrow 0}6(a)^3/3 = 2(1)^3 -\lim_{a \rightarrow 0}2(a)^3 = 2 - 0 = 2\]

  9. anonymous
    • 5 years ago
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    But that's not the correct answer to it!

  10. anonymous
    • 5 years ago
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    thats only half of it though. you have to take the integral of the first half also, i was only showing how to do the limit part.

  11. anonymous
    • 5 years ago
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    do you see? so evaluate \[\int\limits_{-5}^{0}82xdx\] and add two

  12. anonymous
    • 5 years ago
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    answer should be 1027?

  13. anonymous
    • 5 years ago
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    Nope :(

  14. anonymous
    • 5 years ago
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    what is the answer? is it -1023?

  15. anonymous
    • 5 years ago
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    Not even that..

  16. anonymous
    • 5 years ago
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    answer is?

  17. anonymous
    • 5 years ago
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    I can just type in the possible answers to see if thats right or wrong.. It doesn't tell the exact ans though

  18. anonymous
    • 5 years ago
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    okay

  19. anonymous
    • 5 years ago
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    did either work?

  20. anonymous
    • 5 years ago
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    no

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