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    The region R is bounded by the curve y=3x+ \frac 15 \ x^3 , the x axis and the lines x=1, x=3. Find the area of R.

    I've been able to do all questions on our integration homework apart from this one as this is the only one without a diagram? I tried drawing one but I can't draw a cubic graph- should I learn how to draw one, or can I do the question without drawing a diagram?

    Any tips on how I could go about working this out? thanks very much guys
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    Provided that y is positive throughout the interval 1 to 3 then just do the integral. This function is positive through the interval.
    The reason that y must be >0 throughout is that areas below the x axis would be negative. Usually, you have to find the absolute area and so if your curve dips below the x axis, you have to find that region separately (it will be negative for x>0) and just add on the magnitude ignoring the sign.
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    (Original post by Lid-the-squid)
    The region R is bounded by the curve y=3x+ \frac 15 \ x^3 , the x axis and the lines x=1, x=3. Find the area of R.

    I've been able to do all questions on our integration homework apart from this one as this is the only one without a diagram? I tried drawing one but I can't draw a cubic graph- should I learn how to draw one, or can I do the question without drawing a diagram?

    Any tips on how I could go about working this out? thanks very much guys
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    (Original post by Lid-the-squid)
    The region R is bounded by the curve y=3x+ \frac 15 \ x^3 , the x axis and the lines x=1, x=3. Find the area of R.

    I've been able to do all questions on our integration homework apart from this one as this is the only one without a diagram? I tried drawing one but I can't draw a cubic graph- should I learn how to draw one, or can I do the question without drawing a diagram?

    Any tips on how I could go about working this out? thanks very much guys
    This is one of those questions where the best approach is "just do it"! It won't do you any harm to learn how to sketch cubics but for this function in such a limited range of values it won't teach you anything enlightening

    y is positive between the two x values, so just integrate the function, sub in the limits and take the difference between the two values.
 
 
 
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