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Math Help - Maths help for integration

  1. #1
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    Unhappy Maths help for integration

    hey i do not know how to do this question. I don't know how to simplify the power of 3.

    Find the area enclosed between the curve y = x^3 , the x - axis and the line y = -3 x + 4.

    the answer is 0.42 units^2.

    thank you.
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  2. #2
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    You need to find

     <br />
\int_0^ax^3~dx+\int_a^{\frac{4}{3}}-3x+4~dx<br />

    a is where x^3 = -3x+4
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  3. #3
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    hey i don't get what you mean.

    sorry
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  4. #4
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    Quote Originally Posted by pickslides View Post
    You need to find

     <br />
\int_0^ax^3~dx+\int_a^{\frac{4}{3}}-3x+4~dx<br />

    a is where x^3 = -3x+4

    hey i know how to do it but the thing it i dont know how to find the x^3 + 3x -4 = 0 how do you simplify that to find the x - values ?
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  5. #5
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    Re: Maths help for integration

    Quote Originally Posted by maay View Post
    hey i know how to do it but the thing it i dont know how to find the x^3 + 3x -4 = 0 how do you simplify that to find the x - values ?
    It should be clear by inspection that x = 1 satisfies the equation. Therefore x - 1 is a factor of x^3 + 3x - 4 and anyone studying calculus should be able to factorise a cubic if a linear factor is known and therefore establish that x = 1 is the only real solution.
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