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anonymous

  • 5 years ago

prove that the intgrale from a to b for f(x)=x is =b^2 -a^2/2.

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  1. anonymous
    • 5 years ago
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    prove \[\int\limits_{a}^{b}x dx=b^{2}-a ^{2}/2\]

  2. anonymous
    • 5 years ago
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    Proof Strategy: Use the eu du = eu + C since eln b = b, bx dx = [ (eln b) x ] dx = e (ln b) x dx set u = (ln b) x then du = (ln b) dx substitute... = eu (du / ln b) = (1 / ln b) eu du solve the integral... = (1 / ln b) ( eu + C ) = (1 / ln b) eu + C2 (create new constant) substitute back u = (ln b) x, = ( 1 / ln b) e(ln b) x + C2 = ( 1 / ln b) ( e(ln b) )x + C2 = ( 1 / ln b) bx + C2 = bx / ln b + C2 Q.E.D. 2. You need not memorize this theorem. Derive it each time you use it. Consider this example: if you have the integral: 2x dx. There is no need to memorize the formula. We will get this integral into the easier form, eu du. Recall that eln(2) = 2 2x dx = ( eln (2) ) x dx = eln (2) x dx set u = ln(2) x then du = ln(2) dx substitute: = eu (du / ln 2 ) = (1 / ln 2) eu du = (1 / ln 2) eu + C substitute back... = (1 / ln 2) eln(2) x + C = (1 / ln 2) ( eln(2) )x + C = (1 / ln 2) 2x + C ANSWER

  3. anonymous
    • 5 years ago
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    deos that help

  4. anonymous
    • 5 years ago
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    srry my key bored is bad

  5. anonymous
    • 5 years ago
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    yes thanx ,but am still stuck how to prove it

  6. anonymous
    • 5 years ago
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    umm i see i some time need help on that to umm

  7. anonymous
    • 5 years ago
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    i kow hold on i know some won who may help

  8. anonymous
    • 5 years ago
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    like my friend seid just follow the rule of integal :)

  9. anonymous
    • 5 years ago
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    that is how

  10. anonymous
    • 5 years ago
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    and he seid intgrale x dx = x^2/2

  11. anonymous
    • 5 years ago
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    well that was better

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