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Math Help - Integrals

  1. #1
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    Integrals

    The marginal cost of manufacturing x yards of a certain fabric is C'(x)=3-0.01x+0.000006x^2 ( in dollars per yard ). Find the increase in cost if the production level is raised from 500 yards to 5000 yards.

    and

    fnInt((x^3 +3 + 1/(x^2+1))dx)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sw3etazngyrl View Post
    The marginal cost of manufacturing x yards of a certain fabric is C'(x)=3-0.01x+0.000006x^2 ( in dollars per yard ). Find the increase in cost if the production level is raised from 500 yards to 5000 yards.
    I suppose for this one you want:

    \int_{500}^{5000} \left( 3 - 0.01x + 0.000006x^2 \right)dx

    that is not a hard function to integrate. just use the power rule. unless you should be calculating something else. the only place i encountered things like "marginal cost" and such was in a microeconomics class, and we never used calculus at all, so i'm not sure how to relate everything


    and

    fnInt((x^3 +3 + 1/(x^2+1))dx)
    what do you mean "fnInt"?
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  3. #3
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    fnInt means integral
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sw3etazngyrl View Post
    fnInt means integral
    ok. again, most of this integral is simple, you use the power rule. but you also have to know something else.


    Power Rule: \int x^n dx = \frac {x^{n+1}}{n+ 1} + C for n \neq -1

    Something else: \int \frac {1}{x^2 + 1}dx = \arctan x + C


    So,

    \int \left(x^3 + 3 + \frac {1}{x^2 + 1} \right)dx = \frac {1}{4}x^4 + 3x + \arctan x + C


    Now, can you do the first?
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