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Math Help - Finding the region under a curve

  1. #1
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    Angry Finding the region under a curve

    I have two questions here.

    1. Find area of region that lies under curve y=(3x+4)1/2 over 0<x<4
    (Those are less than or equal to signs)

    2. It is estimated that t days from now a farmers crop will be increasing at the rate of .3t2+.6t+1 bushels per day. By how much will the value of the crop increase during the next 5 days if the market price remains fixed at $3 a bushel?


    If you can do step by step, I really don't understand this.
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  2. #2
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    Re: Finding the region under a curve

    Surely you know that the area under a curve f(x) between two points a and b can be calculated using \displaystyle \int_a^b{f(x)\,dx} = F(b) - F(a), where F(x) is an antiderivative of f(x)...
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  3. #3
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    Re: Finding the region under a curve

    I have trouble finding the antiderivatives.
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  4. #4
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    Re: Finding the region under a curve

    For first one make substitution 3x + 4 = u that gives dx = du/3 and the limits will be from 4 to 16
    the question reduces to 1/3 Integral from 4 to 16 ( u^1/2 0 du.
    Now you cal finish it.
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