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

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

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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prove \[\int\limits_{a}^{b}x dx=b^{2}-a ^{2}/2\]
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
deos that help

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Other answers:

srry my key bored is bad
yes thanx ,but am still stuck how to prove it
umm i see i some time need help on that to umm
i kow hold on i know some won who may help
like my friend seid just follow the rule of integal :)
that is how
and he seid intgrale x dx = x^2/2
well that was better

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